void OutputBands()
{
KptList ks = KMesh;
using (StreamWriter w = new StreamWriter("eigenvalues.k"))
{
w.WriteLine("# Grid");
w.WriteLine("{0} {1} {2} {3} {4} {5}", ks.Mesh[0], ks.Mesh[1], ks.Mesh[2],
ks.Shift[0], ks.Shift[1], ks.Shift[2]);
w.WriteLine("# Eigenvalues");
for (int i = 0; i < ks.AllKpts.Count; i++)
{
KPoint kpt = ks.AllKpts[i];
w.Write("{0} {1} {2} ",
kpt.Value.X, kpt.Value.Y, kpt.Value.Z);
for (int j = 0; j < kpt.Wavefunctions.Count; j++)
{
w.Write("{0} ", kpt.Wavefunctions[j].Energy);
}
w.WriteLine();
}
}
}
BandTetrahedron GetTetrahedron(TightBinding tb, KPoint kpt, KptList kpts)
{
List <Pair <int, double> > lst = new List <Pair <int, double> >();
double[] weights = new double[kpts.Kpts.Count];
for (int j = 0; j < kpts.Kpts.Count; j++)
{
double distance = CalcDistance(tb, kpts.Kpts[j].Value, kpt.Value);
weights[j] = 1 / (distance + 0.00001);
}
for (int j = 0; j < weights.Length; j++)
{
lst.Add(new Pair <int, double>(j, weights[j]));
}
lst.Sort((x, y) => { return(y.Second.CompareTo(x.Second)); });
lst.RemoveRange(4, lst.Count - 4);
List <int> ilist = lst.Select(x => x.First).ToList();
BandTetrahedron retval = new BandTetrahedron(tb, kpt.Value, kpts, ilist);
return(retval);
}
void WriteBands(TightBinding tb, KptList kpts, StreamWriter w)
{
int bandCount = kpts.Kpts[0].Wavefunctions.Count;
BandTetrahedron tet = null;
for (int i = 0; i < tb.KPath.Kpts.Count; i++)
{
var kpt = tb.KPath.Kpts[i];
if (tet == null || tet.Contains(kpt) == false)
{
GetTetrahedron(tb, kpt, kpts);
}
w.Write(i);
w.Write(" ");
for (int band = 0; band < bandCount; band++)
{
double energy = tet.Interpolate(kpt);
w.Write("{0} ", energy);
}
w.WriteLine();
}
}
public KptList Clone()
{
KptList retval = new KptList();
retval.allKpts.AddRange(allKpts.Select(x => x.Clone()));
retval.kpts.AddRange(kpts.Select(x => x.Clone()));
if (mesh != null)
{
retval.mesh = (int[])mesh.Clone();
}
if (shift != null)
{
retval.shift = (int[])shift.Clone();
}
retval.gammaCentered = gammaCentered;
foreach (KeyValuePair <int, int> var in Nvalues)
{
retval.Nvalues.Add(var.Key, var.Value);
}
foreach (KeyValuePair <int, int> var in AllNvalues)
{
retval.AllNvalues.Add(var.Key, var.Value);
}
retval.sdir = sdir;
retval.tdir = tdir;
retval.origin = origin;
return(retval);
}
private void RpaChi0Thread(object obj)
{
RpaThreadInfo info = (RpaThreadInfo)obj;
System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
watch.Start();
TightBinding tb = info.tb;
List <RpaParams> rpa = info.RpaParams;
KptList qpts = info.qpts;
for (int i = 0; i < rpa.Count; i++)
{
SetTemperature(tb, rpa[i].Temperature, rpa[i].ChemicalPotential);
rpa[i].X0 = CalcX0(tb, rpa[i].Frequency, qpts.Kpts[rpa[i].Qindex]);
if (i == 0 && info.PrimaryThread)
{
long time = watch.ElapsedTicks * rpa.Count;
TimeSpan s = new TimeSpan(time);
Output.WriteLine("Estimated total time {0:+hh.mm}", s);
}
Complex val = rpa[i].X0.Trace();
Output.Write("q = {0}, T = {1:0.000}, mu = {2:0.000}, omega = {3:0.0000}",
rpa[i].Qindex + 1, rpa[i].Temperature, rpa[i].ChemicalPotential, rpa[i].Frequency);
Output.WriteLine(", Tr(X_0) = {0}", val.ToString("0.0000"));
}
}
void OutputBands(TightBinding tb, KptList ks,
List <RpaParams> rpa, MatrixGetter g, string name)
{
using (StreamWriter w = new StreamWriter("eigenvalues." + name + ".q"))
{
w.WriteLine("# Grid");
w.WriteLine("{0} {1} {2} {3} {4} {5}", ks.Mesh[0], ks.Mesh[1], ks.Mesh[2],
ks.Shift[0], ks.Shift[1], ks.Shift[2]);
w.WriteLine("# Eigenvalues");
foreach (var rpa_i in rpa)
{
var qpt = rpa_i.QptValue;
w.Write("{0} {1} {2} ",
qpt.X, qpt.Y, qpt.Z);
Matrix chi = g(rpa_i);
Matrix evalues = chi.EigenValues();
for (int j = 0; j < evalues.Rows; j++)
{
w.Write("{0} ", evalues[j, 0].RealPart);
}
w.WriteLine();
}
}
}
public void WriteGraceHeader(KptList kpath)
{
file.WriteLine("@with g0");
var pairs = kpath.Kpts.Select(
(kpt, index) => new Pair <int, KPoint>(index, kpt)).ToArray();
var pts = (
from val in pairs
where string.IsNullOrEmpty(val.Second.Name) == false
select val
).ToArray();
file.WriteLine("@ xaxis tick spec type both");
file.WriteLine("@ xaxis tick spec {0}", pts.Length);
for (int i = 0; i < pts.Length; i++)
{
string label = pts[i].Second.Name;
if (label.StartsWith("G"))
{
label = @"\xG\f{}" + label.Substring(1);
}
label = label.Replace("$_", @"\s");
label = label.Replace("$^", @"\S");
label = label.Replace("$.", @"\N");
file.WriteLine("@ xaxis tick major {0}, {1}", i, pts[i].First);
file.WriteLine("@ xaxis ticklabel {0}, \"{1}\"", i, label);
}
}
void CreateBands(TightBinding tb, string name)
{
using (StreamReader r = new StreamReader(name))
{
string line = r.ReadLine();
if (line != "# Grid")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(3);
}
int[] grid = new int[3];
int[] shift = new int[3];
ParseGrid(grid, shift, line);
if (line != "# Eigenvalues")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(2);
}
KptList kpts = new KptList();
kpts.Mesh = grid;
kpts.Shift = shift;
while (r.EndOfStream == false)
{
line = r.ReadLine();
string[] elements = line.Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
KPoint kpt = new KPoint(new Vector3(double.Parse(elements[0]),
double.Parse(elements[1]),
double.Parse(elements[2])));
for (int i = 3; i < elements.Length; i++)
{
Wavefunction wfk = new Wavefunction(0);
wfk.Energy = double.Parse(elements[i]);
kpt.Wavefunctions.Add(wfk);
}
kpts.Kpts.Add(kpt);
}
CreateTetrahedronMesh(kpts);
string outputfile = name + ".bands";
using (StreamWriter w = new StreamWriter(outputfile))
{
WriteBands(tb, kpts, w);
}
}
}
void CreateBands(TightBinding tb, string name)
{
using (StreamReader r = new StreamReader(name))
{
string line = r.ReadLine();
if (line != "# Grid")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(3);
}
int[] grid = new int[3];
int[] shift = new int[3];
ParseGrid(grid, shift, line);
if (line != "# Eigenvalues")
{
Console.WriteLine("Not an eigenvalues file!");
System.Environment.Exit(2);
}
KptList kpts = new KptList();
kpts.Mesh = grid;
kpts.Shift = shift;
while (r.EndOfStream == false)
{
line = r.ReadLine();
string[] elements = line.Split(new char[] { ' '}, StringSplitOptions.RemoveEmptyEntries );
KPoint kpt = new KPoint(new Vector3(double.Parse(elements[0]),
double.Parse(elements[1]),
double.Parse(elements[2])));
for (int i = 3; i < elements.Length; i++)
{
Wavefunction wfk = new Wavefunction(0);
wfk.Energy = double.Parse(elements[i]);
kpt.Wavefunctions.Add(wfk);
}
kpts.Kpts.Add(kpt);
}
CreateTetrahedronMesh(kpts);
string outputfile = name + ".bands";
using (StreamWriter w = new StreamWriter(outputfile))
{
WriteBands(tb, kpts, w);
}
}
}
public static KptPlane GeneratePlane(Lattice lattice, Vector3[] points, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptPlane retval = new KptPlane();
retval.SetLattice(lattice);
retval.mesh = (int[])qmesh.Mesh.Clone();
retval.shift = new int[3];
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = diff_2;
NormalizeST(lattice, retval);
int zmax = qmesh.Mesh[2] * 2;
int ymax = qmesh.Mesh[1] * 2;
int xmax = qmesh.Mesh[0] * 2;
List <KPoint> planePoints = new List <KPoint>();
for (int i = 0; i < qmesh.Kpts.Count; i++)
{
var qpt = qmesh.Kpts[i];
Vector3 diff = lattice.ReciprocalExpand(qpt.Value) - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
retval.AddKpt(qpt);
}
}
// now sort q-points to lay them in the s,t plane.
retval.SortKpoints();
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return(retval);
}
public static KptPlane GeneratePlane(Lattice lattice, Vector3[] points, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptPlane retval = new KptPlane();
retval.SetLattice(lattice);
retval.mesh = (int[])qmesh.Mesh.Clone();
retval.shift = new int[3];
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = diff_2;
NormalizeST(lattice, retval);
int zmax = qmesh.Mesh[2] * 2;
int ymax = qmesh.Mesh[1] * 2;
int xmax = qmesh.Mesh[0] * 2;
List<KPoint> planePoints = new List<KPoint>();
for (int i = 0; i < qmesh.Kpts.Count; i++)
{
var qpt = qmesh.Kpts[i];
Vector3 diff = lattice.ReciprocalExpand(qpt.Value) - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
retval.AddKpt(qpt);
}
}
// now sort q-points to lay them in the s,t plane.
retval.SortKpoints();
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return retval;
}
void ReadKPathSection(string section, ref KptList path)
{
if (path != null)
{
ThrowEx(section + " found twice.");
}
Vector3 lastKpt = Vector3.Zero;
char[] array = new char[] { ' ' };
const double ptScale = 400;
int ptCount = 0;
path = new KptList();
while (EOF == false && LineType != LineType.NewSection)
{
double dummy;
string[] vals = Line.Split(array, StringSplitOptions.RemoveEmptyEntries);
if (vals.Length != 3 && vals.Length != 4)
{
ThrowEx("Cannot understand path entry.");
}
string text = Line;
string name = string.Empty;
if (double.TryParse(vals[0], out dummy) == false)
{
text = text.Substring(text.IndexOf(' '));
name = vals[0];
}
Vector3 vecval = Vector3.Parse(text);
Vector3 kpt = vecval;
double length = (kpt - lastKpt).Magnitude;
if (ptCount == 0)
{
path.AddPts(kpt, kpt, 1);
}
else
{
path.AddPts(lastKpt, kpt, Math.Max((int)(ptScale * length), 1));
}
path.Kpts[path.Kpts.Count - 1].Name = name;
ptCount++;
lastKpt = kpt;
ReadNextLine();
}
}
private static void NormalizeST(Lattice lattice, KptList retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).Magnitude;
retval.tdir /= GammaInDirection(lattice, retval.tdir).Magnitude;
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
private void CalcNelec()
{
KptList ks = KMesh;
Matrix[] eigenvals = new Matrix[ks.Kpts.Count];
for (int i = 0; i < KMesh.Kpts.Count; i++)
{
Matrix vals = new Matrix(Orbitals.Count, Orbitals.Count);
for (int j = 0; j < Orbitals.Count; j++)
{
vals[j, 0] = ks.Kpts[i].Wavefunctions[j].Energy;
}
eigenvals[i] = vals;
}
double beta = 1 / TemperatureMesh[0];
double N = FindNelec(ks, eigenvals, MuMesh[0], beta);
if (specifiedNelec)
{
MuMesh = new double[Nelec.Length];
for (int i = 0; i < MuMesh.Length; i++)
{
MuMesh[i] = FindMu(ks, eigenvals, Nelec[i], beta);
}
}
else
{
Nelec = new double[MuMesh.Length];
for (int i = 0; i < MuMesh.Length; i++)
{
Nelec[i] = FindNelec(ks, eigenvals, MuMesh[i], beta);
}
}
Output.WriteLine(" mu Nelec");
for (int i = 0; i < MuMesh.Length; i++)
{
MuMesh[i] = FindMu(ks, eigenvals, Nelec[i], beta);
Output.WriteLine(" {0:0.000000} {1:0.000000}", MuMesh[i], Nelec[i]);
}
}
public static KptList DefaultPath(Lattice l)
{
const int pts = 40;
KptList retval = new KptList();
retval.Kpts.Add(new KPoint(Vector3.Zero));
retval.AddPts(Vector3.Zero, l.G1 * Math.PI, pts);
retval.AddPts(l.G1 * Math.PI, (l.G1 + l.G2) * Math.PI, pts);
retval.AddPts((l.G1 + l.G2) * Math.PI, l.G2 * Math.PI, pts);
retval.AddPts(l.G2 * Math.PI, l.G3 * Math.PI, pts);
retval.AddPts(l.G3 * Math.PI, Vector3.Zero, pts);
return retval;
}
public static KptList DefaultPath(Lattice l)
{
const int pts = 40;
KptList retval = new KptList();
retval.Kpts.Add(new KPoint(Vector3.Zero));
retval.AddPts(Vector3.Zero, l.G1 * Math.PI, pts);
retval.AddPts(l.G1 * Math.PI, (l.G1 + l.G2) * Math.PI, pts);
retval.AddPts((l.G1 + l.G2) * Math.PI, l.G2 * Math.PI, pts);
retval.AddPts(l.G2 * Math.PI, l.G3 * Math.PI, pts);
retval.AddPts(l.G3 * Math.PI, Vector3.Zero, pts);
return(retval);
}
private Matrix[] CalcGreenFunction(TightBindingSuite.TightBinding tb, RpaParams p, KptList kmesh)
{
int orbitalCount = tb.Orbitals.Count;
Matrix[] retval = new Matrix[kmesh.Kpts.Count];
Complex denomFactor = new Complex(0, p.Temperature);
for (int k = 0; k < kmesh.Kpts.Count; k++)
{
retval[k] = new Matrix(orbitalCount, orbitalCount);
Matrix hamilt = tb.CalcHamiltonian(kmesh.Kpts[k].Value);
Matrix vals, vecs;
hamilt.EigenValsVecs(out vals, out vecs);
for (int i = 0; i < orbitalCount; i++)
{
for (int j = 0; j < orbitalCount; j++)
{
for (int n = 0; n < orbitalCount; n++)
{
var wfk = new Wavefunction(orbitalCount);
wfk.Energy = vals[n, 0].RealPart;
for (int c = 0; c < vecs.Rows; c++)
{
wfk.Coeffs[c] = vecs[c, n];
}
Complex coeff =
wfk.Coeffs[i].Conjugate() *
wfk.Coeffs[j];
Complex g = 1.0 / (p.Frequency + p.ChemicalPotential - wfk.Energy + denomFactor);
retval[k][i, j] += g * coeff;
}
}
}
}
return retval;
}
private double FindNelec(KptList ks, Matrix[] eigenvals, double mu, double beta)
{
double N = 0;
for (int i = 0; i < ks.Kpts.Count; i++)
{
double weight = ks.Kpts[i].Weight;
for (int j = 0; j < eigenvals[i].Rows; j++)
{
double energy = eigenvals[i][j, 0].RealPart;
double npt = 2 * FermiFunction(energy, mu, beta);
N += npt * weight;
}
}
return(N);
}
private void GenerateKmesh()
{
tb.kmesh = KptList.GenerateMesh(tb.lattice, tb.kgrid, tb.kshift, tb.symmetries, false);
Output.WriteLine("Applied {0} symmetries to get {1} irreducible kpoints from {2}.",
tb.symmetries.Count, tb.kmesh.Kpts.Count, tb.kmesh.AllKpts.Count);
using (StreamWriter writer = new StreamWriter("kpts"))
{
for (int i = 0; i < tb.kmesh.Kpts.Count; i++)
{
Vector3 red = tb.lattice.ReducedCoords(tb.kmesh.Kpts[i].Value);
writer.WriteLine("{0} {1}", i, red);
}
}
if (tb.UseQPlane == false)
{
tb.qmesh = KptList.GenerateMesh(tb.lattice, tb.qgrid, tb.qshift,
tb.symmetries, false);
Output.WriteLine("Found {0} qpoints in the zone.", tb.qmesh.Kpts.Count);
}
if (tb.setQplane)
{
tb.qplane = KptList.GeneratePlane(tb.lattice, tb.qplaneDef, tb.symmetries, tb.qgrid, null);
Output.WriteLine("Found {0} irreducible qpoints in the plane of {1} qpoints.",
tb.qplane.Kpts.Count, tb.qplane.AllKpts.Count);
using (StreamWriter writer = new StreamWriter("qpts"))
{
for (int i = 0; i < tb.qplane.Kpts.Count; i++)
{
Vector3 red = tb.lattice.ReducedCoords(tb.qplane.Kpts[i].Value);
writer.WriteLine("{0} {1}", i, red);
}
}
}
}
public BandTetrahedron(TightBinding tb, Vector3 anchor, KptList kpts, List<int> indices)
{
for (int i = 0; i < indices.Count; i++)
{
KPoint kpt = kpts.Kpts[indices[i]].Clone();
Vector3 delta = kpt.Value - anchor;
ShiftDelta(ref delta, tb.Lattice.G1);
ShiftDelta(ref delta, tb.Lattice.G2);
ShiftDelta(ref delta, tb.Lattice.G3);
kpt.Value = delta + anchor;
this.kpts.Add(kpt);
}
CalculateVelocityMatrix();
}
public BandTetrahedron(TightBinding tb, Vector3 anchor, KptList kpts, List <int> indices)
{
for (int i = 0; i < indices.Count; i++)
{
KPoint kpt = kpts.Kpts[indices[i]].Clone();
Vector3 delta = kpt.Value - anchor;
ShiftDelta(ref delta, tb.Lattice.G1);
ShiftDelta(ref delta, tb.Lattice.G2);
ShiftDelta(ref delta, tb.Lattice.G3);
kpt.Value = delta + anchor;
this.kpts.Add(kpt);
}
CalculateVelocityMatrix();
}
public void RunRpa(TightBinding tb, KptList qpts, bool plane)
{
List <KPoint> QMesh = qpts.Kpts;
List <RpaParams> rpa = CreateRpaParameterList(tb, QMesh);
Output.WriteLine("Calculating susceptibility for {0} q-points.", QMesh.Count);
CalcSusceptibility(tb, qpts, rpa);
if (plane)
{
SaveMatricesQPlane(tb, QMesh, rpa, x => x.X0, "chi_0");
SaveMatricesQPlane(tb, QMesh, rpa, x => x.Xs, "chi_s");
SaveMatricesQPlane(tb, QMesh, rpa, x => x.Xc, "chi_c");
}
else
{
OutputBands(tb, qpts, rpa, CalcX0 => CalcX0.X0, "chi_0");
}
}
public void RunRpa(TightBinding tb, KptList qpts, bool plane)
{
List<KPoint> QMesh = qpts.Kpts;
List<RpaParams> rpa = CreateRpaParameterList(tb, QMesh);
Output.WriteLine("Calculating susceptibility for {0} q-points.", QMesh.Count);
CalcSusceptibility(tb, qpts, rpa);
if (plane)
{
SaveMatricesQPlane(tb, QMesh, rpa, x => x.X0, "chi_0");
SaveMatricesQPlane(tb, QMesh, rpa, x => x.Xs, "chi_s");
SaveMatricesQPlane(tb, QMesh, rpa, x => x.Xc, "chi_c");
}
else
{
OutputBands(tb, qpts, rpa, CalcX0 => CalcX0.X0, "chi_0");
}
}
void Run(string inputfile)
{
using (StreamWriter w = new StreamWriter("gplot.out"))
{
Output.SetFile(w);
TightBindingSuite.TightBinding tb = new TightBindingSuite.TightBinding();
tb.LoadTB(inputfile);
RpaParams p = new RpaParams(0, Vector3.Zero, tb.TemperatureMesh[0], tb.FrequencyMesh[0], tb.MuMesh[0]);
KptList kmesh = KptList.GenerateMesh(
tb.Lattice, tb.KMesh.Mesh, null, tb.Symmetries, true);
Matrix[] green = CalcGreenFunction(tb, p, kmesh);
while (true)
{
WriteGreenFunction(tb, green, kmesh);
};
}
}
void ReadKPathSection(string section, ref KptList path)
{
if (path != null)
ThrowEx(section + " found twice.");
Vector3 lastKpt = Vector3.Zero;
char[] array = new char[] { ' ' };
const double ptScale = 400;
int ptCount = 0;
path = new KptList();
while (EOF == false && LineType != LineType.NewSection)
{
double dummy;
string[] vals = Line.Split(array, StringSplitOptions.RemoveEmptyEntries);
if (vals.Length != 3 && vals.Length != 4)
ThrowEx("Cannot understand path entry.");
string text = Line;
string name = string.Empty;
if (double.TryParse(vals[0], out dummy) == false)
{
text = text.Substring(text.IndexOf(' '));
name = vals[0];
}
Vector3 vecval = Vector3.Parse(text);
Vector3 kpt = vecval;
double length = (kpt - lastKpt).Magnitude;
if (ptCount == 0)
{
path.AddPts(kpt, kpt, 1);
}
else
{
path.AddPts(lastKpt, kpt, Math.Max((int)(ptScale * length), 1));
}
path.Kpts[path.Kpts.Count - 1].Name = name;
ptCount++;
lastKpt = kpt;
ReadNextLine();
}
}
public static KptList oldGenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
bool centerGamma = false;
KptList retval = new KptList();
int zmax = kgrid[2] * 2;
int ymax = kgrid[1] * 2;
int xmax = kgrid[0] * 2;
if (shift == null)
shift = new int[3];
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = centerGamma;
int index = 0;
Vector3 gridVector = new Vector3(kgrid[0], kgrid[1], kgrid[2]);
SymmetryList compatSyms = new SymmetryList();
foreach (var symmetry in syms)
{
Vector3 grid2 = symmetry.Value * gridVector;
for (int gi = 0; gi < 3; gi++)
grid2[gi] = Math.Abs(grid2[gi]);
if (grid2 == gridVector)
{
compatSyms.Add(symmetry);
}
}
for (int k = 0; k <= zmax; k += 2)
{
for (int j = 0; j <= ymax; j += 2)
{
for (int i = 0; i <= xmax; i += 2)
{
if (includeEnds == false)
{
if (k == zmax) break;
if (i == xmax) break;
if (j == ymax) break;
}
int N = retval.KptToInteger(i, j, k);
bool foundSym = false;
double dx = (i + shift[0]) / (double)xmax;
double dy = (j + shift[1]) / (double)ymax;
double dz = (k + shift[2]) / (double)zmax;
int symN = N;
List<int> orbitals = null;
if (centerGamma)
{
if (kgrid[0] > 1) dx -= 0.5;
if (kgrid[1] > 1) dy -= 0.5;
if (kgrid[2] > 1) dz -= 0.5;
}
Vector3 pt = CalcK(lattice, dx, dy, dz);
#if DEBUG
int testi, testj, testk;
retval.ReduceKpt(lattice, new Vector3(pt), out testi, out testj, out testk);
//System.Diagnostics.Debug.Assert(i == testi);
//System.Diagnostics.Debug.Assert(j == testj);
//System.Diagnostics.Debug.Assert(k == testk);
#endif
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * pt;
if (Tpt == pt)
continue;
Vector3 red = lattice.ReducedCoords(Tpt, true);
int newi = (int)Math.Round(xmax * red.X - shift[0]);
int newj = (int)Math.Round(ymax * red.Y - shift[1]);
int newk = (int)Math.Round(zmax * red.Z - shift[2]);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
break;
}
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
retval.allKpts.Add(new KPoint(kptValue));
if (retval.Nvalues.ContainsKey(N))
{
}
else if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
retval.allKpts[i].Weight /= count;
}
if (includeEnds)
{
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
List<int> removeThese = new List<int>();
List<int> equivKpt = new List<int>();
// read this value first, because the size of the array will change.
int kptCount = retval.AllKpts.Count;
for (int kindex = 0; kindex < kptCount; kindex++)
{
if (removeThese.Contains(kindex))
continue;
Vector3 kpt = retval.allKpts[kindex].Value;
double dist = kpt.Magnitude;
equivKpt.Clear();
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
continue;
Vector3 pt = kpt +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double newDist = pt.Magnitude;
if (newDist < dist - 1e-6)
{
foreach (var value in equivKpt)
{
if (removeThese.Contains(value) == false)
removeThese.Add(value);
}
equivKpt.Clear();
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(kindex) == false)
removeThese.Add(kindex);
// break out of the loop
k = 1; j = 1; i = 2;
}
else
{
retval.allKpts[kindex].Value = pt;
kpt = pt;
dist = newDist;
// reset variables since we updated this kpoint value.
k = -1;
j = -1;
i = -2;
}
}
else if (Math.Abs(dist - newDist) < 1e-6)
{
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(search))
{
k = 1; j = 1; i = 2;
removeThese.Add(kindex);
break;
}
equivKpt.Add(search);
continue;
}
equivKpt.Add(retval.allKpts.Count);
retval.allKpts.Add(new KPoint(pt));
}
}
}
}
}
// sort in reverse order
removeThese.Sort((x, y) => -x.CompareTo(y));
for (int i = 0; i < removeThese.Count; i++)
{
retval.allKpts.RemoveAt(removeThese[i]);
}
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
}
#if DEBUG
if (!includeEnds)
{
double check = 0;
for (int i = 0; i < retval.kpts.Count; i++)
check += retval.kpts[i].Weight;
System.Diagnostics.Debug.Assert(Math.Abs(check - 1) < 1e-8);
}
#endif
return retval;
}
void CreateTetrahedronMesh(KptList kpts)
{
}
private double FindMu(KptList ks, Matrix[] eigenvals, double Ntarget, double beta)
{
double N;
double mu_lower, mu_upper;
double N_lower, N_upper;
double mu;
mu_lower = mu_upper = mu = 0;
// first bracket
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
{
mu_upper = mu;
while (mu_lower >= mu_upper)
{
mu -= 1;
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
mu_upper = mu;
else
mu_lower = mu;
}
}
else
{
mu_lower = mu;
while (mu_lower >= mu_upper)
{
mu += 1;
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
mu_upper = mu;
else
mu_lower = mu;
}
}
mu = 0.5 * (mu_upper + mu_lower);
N_lower = FindNelec(ks, eigenvals, mu_lower, beta);
N_upper = FindNelec(ks, eigenvals, mu_upper, beta);
// do linear extrapolation
int iter = 0;
while (Math.Abs(N - Ntarget) > 1e-11 && iter < 300)
{
double slope = (N_upper - N_lower) / (mu_upper - mu_lower);
if ((iter / 3) % 5 < 2)
{
// bisection in case system is gapped at target number
mu = 0.5 * (mu_upper + mu_lower);
}
else
{
// linear extrapoliation
mu = (Ntarget - N_lower) / slope + mu_lower;
}
N = FindNelec(ks, eigenvals, mu, beta);
if (N < Ntarget)
{
mu_lower = mu;
N_lower = N;
}
else if (N > Ntarget)
{
mu_upper = mu;
N_upper = N;
}
iter++;
}
if (iter >= 300)
{
Output.WriteLine("Failed to find chemical potential. Check the number of electrons.");
throw new Exception("Failed to find chemical potential.");
}
return mu;
}
BandTetrahedron GetTetrahedron(TightBinding tb, KPoint kpt, KptList kpts)
{
List<Pair<int, double>> lst = new List<Pair<int, double>>();
double[] weights = new double[kpts.Kpts.Count];
for (int j = 0; j < kpts.Kpts.Count; j++)
{
double distance = CalcDistance(tb, kpts.Kpts[j].Value, kpt.Value);
weights[j] = 1 / (distance + 0.00001);
}
for (int j = 0; j < weights.Length; j++)
{
lst.Add(new Pair<int, double>(j, weights[j]));
}
lst.Sort((x,y) => { return y.Second.CompareTo(x.Second); });
lst.RemoveRange(4, lst.Count - 4);
List<int> ilist = lst.Select(x => x.First).ToList();
BandTetrahedron retval = new BandTetrahedron(tb, kpt.Value, kpts, ilist);
return retval;
}
void DoBandStructure()
{
KptList kpath = KPath;
Output.WriteLine("Computing band structure with {0} k-points.",
kpath.Kpts.Count);
List <Matrix> eigenvals = new List <Matrix>();
List <Matrix> eigenvecs = new List <Matrix>();
for (int i = 0; i < kpath.Kpts.Count; i++)
{
Matrix m = CalcHamiltonian(kpath.Kpts[i]);
Matrix vals, vecs;
m.EigenValsVecs(out vals, out vecs);
eigenvals.Add(vals);
eigenvecs.Add(vecs);
for (int j = 0; j < vals.Rows; j++)
{
if (double.IsNaN(vals[j, 0].RealPart))
{
throw new Exception("NaN found while diagonalizing tight binding at kpt " + i.ToString() + ".");
}
}
}
int datasets = eigenvals[0].Rows;
using (AgrWriter writer = new AgrWriter(outputfile + ".band.agr"))
{
int[] colors = new int[datasets];
for (int i = 0; i < colors.Length; i++)
{
colors[i] = 1;
}
writer.WriteGraceHeader(kpath);
writer.WriteGraceSetLineStyle(0, 2);
writer.WriteGraceSetLineColor(0);
writer.WriteGraceSetLineColor(1, colors);
writer.WriteGraceBaseline(kpath.Kpts.Count);
for (int i = 0; i < datasets; i++)
{
writer.WriteGraceDataset(kpath.Kpts.Count,
x => new Pair <double, double>(x, eigenvals[x][i, 0].RealPart - MuMesh[0]));
}
}
// Do fat bands plot
using (AgrWriter writer = new AgrWriter(outputfile + ".bweights.agr"))
{
// set all band lines to black
int[] colors = new int[datasets];
for (int i = 0; i < colors.Length; i++)
{
colors[i] = 1;
}
writer.WriteGraceHeader(kpath);
writer.WriteGraceSetLineStyle(0, 2);
writer.WriteGraceSetLineColor(0);
writer.WriteGraceSetLineColor(1, colors);
int set = datasets + 1;
for (int j = 0; j < Orbitals.Count; j++)
{
int color = j + 1;
if (color > 15)
{
color -= 15;
}
writer.WriteGraceSetLineColor(set, color);
writer.WriteGraceSetSymbol(set, 1);
writer.WriteGraceSetSymbolColor(set, color);
writer.WriteGraceSetSymbolFill(set, 1);
set++;
}
set = datasets + 1;
for (int j = 0; j < Orbitals.Count; j++)
{
writer.WriteGraceLegend(set, Orbitals[j].Name);
set += 1;
}
writer.WriteGraceBaseline(kpath.Kpts.Count);
for (int i = 0; i < datasets * Orbitals.Count; i++)
{
writer.WriteGraceSetLineStyle(i + datasets + 1, 0);
}
for (int i = 0; i < datasets; i++)
{
writer.WriteGraceDataset(kpath.Kpts.Count,
x => new Pair <double, double>(x, eigenvals[x][i, 0].RealPart - MuMesh[0]));
}
for (int j = 0; j < Orbitals.Count; j++)
{
writer.WriteGraceDataset("xysize", kpath.Kpts.Count * datasets,
x =>
{
int k = x % kpath.Kpts.Count;
int i = x / kpath.Kpts.Count;
double mag = eigenvecs[k][j, i].MagnitudeSquared;
if (mag < 0.0001)
{
return(null);
}
return(new Triplet <double, double, double>(
k,
eigenvals[k][i, 0].RealPart - MuMesh[0],
mag));
});
}
}
}
public static KptList oldGenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
bool centerGamma = false;
KptList retval = new KptList();
int zmax = kgrid[2] * 2;
int ymax = kgrid[1] * 2;
int xmax = kgrid[0] * 2;
if (shift == null)
{
shift = new int[3];
}
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = centerGamma;
int index = 0;
Vector3 gridVector = new Vector3(kgrid[0], kgrid[1], kgrid[2]);
SymmetryList compatSyms = new SymmetryList();
foreach (var symmetry in syms)
{
Vector3 grid2 = symmetry.Value * gridVector;
for (int gi = 0; gi < 3; gi++)
{
grid2[gi] = Math.Abs(grid2[gi]);
}
if (grid2 == gridVector)
{
compatSyms.Add(symmetry);
}
}
for (int k = 0; k <= zmax; k += 2)
{
for (int j = 0; j <= ymax; j += 2)
{
for (int i = 0; i <= xmax; i += 2)
{
if (includeEnds == false)
{
if (k == zmax)
{
break;
}
if (i == xmax)
{
break;
}
if (j == ymax)
{
break;
}
}
int N = retval.KptToInteger(i, j, k);
bool foundSym = false;
double dx = (i + shift[0]) / (double)xmax;
double dy = (j + shift[1]) / (double)ymax;
double dz = (k + shift[2]) / (double)zmax;
int symN = N;
List <int> orbitals = null;
if (centerGamma)
{
if (kgrid[0] > 1)
{
dx -= 0.5;
}
if (kgrid[1] > 1)
{
dy -= 0.5;
}
if (kgrid[2] > 1)
{
dz -= 0.5;
}
}
Vector3 pt = CalcK(lattice, dx, dy, dz);
#if DEBUG
int testi, testj, testk;
retval.ReduceKpt(lattice, new Vector3(pt), out testi, out testj, out testk);
//System.Diagnostics.Debug.Assert(i == testi);
//System.Diagnostics.Debug.Assert(j == testj);
//System.Diagnostics.Debug.Assert(k == testk);
#endif
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * pt;
if (Tpt == pt)
{
continue;
}
Vector3 red = lattice.ReducedCoords(Tpt, true);
int newi = (int)Math.Round(xmax * red.X - shift[0]);
int newj = (int)Math.Round(ymax * red.Y - shift[1]);
int newk = (int)Math.Round(zmax * red.Z - shift[2]);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
{
break;
}
}
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
retval.allKpts.Add(new KPoint(kptValue));
if (retval.Nvalues.ContainsKey(N))
{
}
else if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
retval.allKpts[i].Weight /= count;
}
if (includeEnds)
{
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
List <int> removeThese = new List <int>();
List <int> equivKpt = new List <int>();
// read this value first, because the size of the array will change.
int kptCount = retval.AllKpts.Count;
for (int kindex = 0; kindex < kptCount; kindex++)
{
if (removeThese.Contains(kindex))
{
continue;
}
Vector3 kpt = retval.allKpts[kindex].Value;
double dist = kpt.Magnitude;
equivKpt.Clear();
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
{
continue;
}
Vector3 pt = kpt +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double newDist = pt.Magnitude;
if (newDist < dist - 1e-6)
{
foreach (var value in equivKpt)
{
if (removeThese.Contains(value) == false)
{
removeThese.Add(value);
}
}
equivKpt.Clear();
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(kindex) == false)
{
removeThese.Add(kindex);
}
// break out of the loop
k = 1; j = 1; i = 2;
}
else
{
retval.allKpts[kindex].Value = pt;
kpt = pt;
dist = newDist;
// reset variables since we updated this kpoint value.
k = -1;
j = -1;
i = -2;
}
}
else if (Math.Abs(dist - newDist) < 1e-6)
{
int search = retval.AllKpts.FindIndex(x => (x.Value - pt).Magnitude < 1e-6);
if (search != -1)
{
if (removeThese.Contains(search))
{
k = 1; j = 1; i = 2;
removeThese.Add(kindex);
break;
}
equivKpt.Add(search);
continue;
}
equivKpt.Add(retval.allKpts.Count);
retval.allKpts.Add(new KPoint(pt));
}
}
}
}
}
// sort in reverse order
removeThese.Sort((x, y) => - x.CompareTo(y));
for (int i = 0; i < removeThese.Count; i++)
{
retval.allKpts.RemoveAt(removeThese[i]);
}
retval.allKpts.Sort((x, y) => x.Value.Z.CompareTo(y.Value.Z));
}
#if DEBUG
if (!includeEnds)
{
double check = 0;
for (int i = 0; i < retval.kpts.Count; i++)
{
check += retval.kpts[i].Weight;
}
System.Diagnostics.Debug.Assert(Math.Abs(check - 1) < 1e-8);
}
#endif
return(retval);
}
void WriteBands(TightBinding tb, KptList kpts, StreamWriter w)
{
int bandCount = kpts.Kpts[0].Wavefunctions.Count;
BandTetrahedron tet = null;
for (int i = 0; i < tb.KPath.Kpts.Count; i++)
{
var kpt = tb.KPath.Kpts[i];
if (tet == null || tet.Contains(kpt) == false)
{
GetTetrahedron(tb, kpt, kpts);
}
w.Write(i);
w.Write(" ");
for (int band = 0; band < bandCount; band++)
{
double energy = tet.Interpolate(kpt);
w.Write("{0} ", energy);
}
w.WriteLine();
}
}
private static void NormalizeST(Lattice lattice, KptList retval)
{
retval.sdir /= retval.sdir.Magnitude;
retval.tdir /= retval.tdir.Magnitude;
retval.sdir /= GammaInDirection(lattice, retval.sdir).Magnitude;
retval.tdir /= GammaInDirection(lattice, retval.tdir).Magnitude;
// double them to make s and t 1 at the zone boundary, instead of 0.5.
retval.sdir *= 2;
retval.tdir *= 2;
}
public static KptList GenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
KptList retval = new KptList();
if (shift == null)
shift = new int[3];
for (int i = 0; i < 3; i++)
if (kgrid[i] == 1)
shift[i] = 1;
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = true;
SymmetryList compatSyms = FindCompatibleSymmetries(kgrid, syms);
int index = 0;
for (int k = -kgrid[2] + shift[2]; k <= kgrid[2]; k += 2)
{
for (int j = -kgrid[1] + shift[1]; j <= kgrid[1]; j += 2)
{
for (int i = -kgrid[0] + shift[0]; i <= kgrid[0]; i += 2)
{
if (includeEnds == false)
{
if (k == kgrid[2]) break;
if (j == kgrid[1]) break;
if (i == kgrid[0]) break;
}
double dx = i * 0.5 / kgrid[0];
double dy = j * 0.5 / kgrid[1];
double dz = k * 0.5 / kgrid[2];
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
int N = retval.KptToInteger(i, j, k);
int symN = N;
System.Diagnostics.Debug.Assert(!(retval.Nvalues.ContainsKey(N) && includeEnds == false));
List<int> orbitals = null;
bool foundSym = false;
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * kptValue;
if (Tpt == kptValue)
continue;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (Math.Abs(newi) % 2 != shift[0] ||
Math.Abs(newj) % 2 != shift[1] ||
Math.Abs(newk) % 2 != shift[2])
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
break;
}
}
if (includeEnds)
{
if (retval.AllNvalues.ContainsKey(N))
{
retval.allKpts.Add(new KPoint(kptValue));
continue;
}
}
retval.AllNvalues.Add(N, retval.allKpts.Count);
retval.allKpts.Add(new KPoint(kptValue));
if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
}
for (int i = 0; i < retval.allKpts.Count; i++)
{
retval.allKpts[i].Weight /= count;
}
return retval;
}
private static bool CenterOnGamma(Lattice lattice, ref KPoint qpt, KptList list)
{
double dist = qpt.Value.Magnitude;
double olddist = dist;
Vector3 newPt = qpt.Value;
bool retval = true;
double bs, bt;
list.GetPlaneST(qpt, out bs, out bt);
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
continue;
Vector3 pt = qpt.Value +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double s, t;
bool valid = list.GetPlaneST(new KPoint(pt), out s, out t);
if (!valid)
continue;
if (pt.Magnitude < dist - 1e-6)
{
if (list.allKpts.Any(x => Math.Abs((x.Value - pt).Magnitude) > 1e-6))
{
retval = false;
continue;
}
dist = pt.Magnitude;
newPt = pt;
}
}
}
}
if (olddist != dist)
retval = true;
if (retval == false)
return false;
qpt.Value = newPt;
return true;
}
private void WriteGreenFunction(TightBindingSuite.TightBinding tb, Matrix[] green, KptList kmesh)
{
WriteGreenFunctionPlane(tb, green, kmesh);
}
private void WriteGreenFunctionPlane(TightBindingSuite.TightBinding tb, Matrix[] green, KptList kmesh)
{
Console.WriteLine("Output as a plane.");
Console.WriteLine();
Console.WriteLine("Enter vectors as a series of three numbers, like: 1 1 0");
Console.WriteLine("Only integer values need be used.");
Console.WriteLine();
Console.Write("Enter first vector: ");
string first = Console.ReadLine();
if (string.IsNullOrEmpty(first))
return;
Console.Write("Enter second vector: ");
string second = Console.ReadLine();
Vector3 sdir = Vector3.Parse(first);
Vector3 tdir = Vector3.Parse(second);
Vector3 udir = Vector3.CrossProduct(sdir, tdir);
Console.Write("Enter origin point: ");
string origin = Console.ReadLine();
Vector3 orig = Vector3.Parse(origin);
Vector3 closestKpt = Vector3.Zero;
double closestDistance = 999999999;
foreach (var kpt in kmesh.AllKpts)
{
double distance = (kpt.Value - orig).MagnitudeSquared;
if (distance < closestDistance)
{
closestKpt = kpt.Value;
closestDistance = distance;
}
}
if (closestDistance > 1e-6)
{
Console.WriteLine("Using closest k-point to specified origin: {0}.", closestKpt);
orig = closestKpt;
sdir += closestKpt;
tdir += closestKpt;
}
KptList plane = KptList.GeneratePlane(
tb.Lattice, new Vector3[] { orig, sdir, tdir }, tb.Symmetries, kmesh);
string tr_filename = string.Format("green.tr.pln");
StreamWriter tr = new StreamWriter(tr_filename);
double lastt = double.MinValue;
for (int k = 0; k < plane.AllKpts.Count; k++)
{
Complex trValue = new Complex();
for (int i = 0; i < green[k].Rows; i++)
{
trValue += green[k][i, i];
}
Vector3 kpt = plane.AllKpts[k].Value;
List<int> orbitalMap;
double s, t;
plane.GetPlaneST(plane.AllKpts[k], out s, out t);
int kindex = kmesh.IrreducibleIndex(kpt, tb.Lattice, tb.Symmetries, out orbitalMap);
if (Math.Abs(t - lastt) > 1e-6)
{
tr.WriteLine();
lastt = t;
}
tr.WriteLine("{0}\t{1}\t{2}", s, t, -trValue.ImagPart);
}
tr.Close();
for (int i = 0; i < green[0].Rows; i++)
{
for (int j = 0; j < green[0].Columns; j++)
{
string re_filename = string.Format("green.re.{0}.{1}.pln", i,j);
string im_filename = string.Format("green.im.{0}.{1}.pln", i, j);
string mag_filename = string.Format("green.mag.{0}.{1}.pln", i, j);
StreamWriter rew = new StreamWriter(re_filename);
StreamWriter imw = new StreamWriter(im_filename);
StreamWriter mag = new StreamWriter(mag_filename);
try
{
lastt = double.MaxValue;
for (int k = 0; k < plane.AllKpts.Count; k++)
{
Vector3 kpt = plane.AllKpts[k].Value;
List<int> orbitalMap;
double s, t;
plane.GetPlaneST(plane.AllKpts[k], out s, out t);
int kindex = kmesh.IrreducibleIndex(kpt, tb.Lattice, tb.Symmetries, out orbitalMap);
if (Math.Abs(t - lastt) > 1e-6)
{
rew.WriteLine();
imw.WriteLine();
mag.WriteLine();
lastt = t;
}
rew.WriteLine("{0}\t{1}\t{2}", s, t, green[kindex][i, j].RealPart);
imw.WriteLine("{0}\t{1}\t{2}", s, t, -green[kindex][i, j].ImagPart);
mag.WriteLine("{0}\t{1}\t{2}", s, t, green[kindex][i, j].Magnitude);
}
}
finally
{
rew.Dispose();
imw.Dispose();
mag.Dispose();
}
}
}
}
void OutputBands(TightBinding tb, KptList ks,
List<RpaParams> rpa, MatrixGetter g, string name)
{
using (StreamWriter w = new StreamWriter("eigenvalues." + name + ".q"))
{
w.WriteLine("# Grid");
w.WriteLine("{0} {1} {2} {3} {4} {5}", ks.Mesh[0], ks.Mesh[1], ks.Mesh[2],
ks.Shift[0], ks.Shift[1], ks.Shift[2]);
w.WriteLine("# Eigenvalues");
foreach(var rpa_i in rpa)
{
var qpt = rpa_i.QptValue;
w.Write("{0} {1} {2} ",
qpt.X, qpt.Y, qpt.Z);
Matrix chi = g(rpa_i);
Matrix evalues = chi.EigenValues();
for (int j = 0; j < evalues.Rows; j++)
{
w.Write("{0} ", evalues[j, 0].RealPart);
}
w.WriteLine();
}
}
}
private void CalcSusceptibility(TightBinding tb, KptList qpts, List <RpaParams> rpa)
{
Matrix ident = Matrix.Identity(tb.Orbitals.Count * tb.Orbitals.Count);
Matrix[] S, C;
CalcSpinChargeMatrices(tb, rpa, out S, out C);
Output.WriteLine("Calculating X0...");
RpaThreadInfo[] threadInfos = CreateThreadInfos(tb, rpa, qpts);
Output.WriteLine("Using {0} threads.", threads);
for (int i = 0; i < threadInfos.Length; i++)
{
RunRpaThread(threadInfos[i]);
if (i == 0)
{
Thread.Sleep(20);
}
}
bool threadsRunning;
do
{
threadsRunning = false;
for (int i = 0; i < threadInfos.Length; i++)
{
if (threadInfos[i].Thread.ThreadState == ThreadState.Running)
{
threadsRunning = true;
}
}
Thread.Sleep(10);
} while (threadsRunning);
Output.WriteLine();
Output.WriteLine("Bare susceptibility calculation completed.");
Output.WriteLine();
double factor = InteractionAdjustment(rpa, S, C, tb);
if (tb.Interactions.AdjustInteractions)
{
Output.WriteLine("Multiplying interactions by {0}.", factor);
for (int i = 0; i < rpa.Count; i++)
{
S[i] *= factor;
C[i] *= factor;
}
}
else if (factor < 1)
{
Output.WriteLine("WARNING: There will be divergent geometric series.");
Output.WriteLine(" Interpret results with care!");
}
Output.WriteLine();
Output.WriteLine("Calculating dressed susceptibilities.");
Output.WriteLine();
RpaParams largestParams = null;
double largest = 0;
string indices = "";
bool charge = false;
for (int i = 0; i < rpa.Count; i++)
{
Matrix s_denom = (ident - S[i] * rpa[i].X0);
Matrix c_denom = (ident + C[i] * rpa[i].X0);
Matrix s_inv = s_denom.Invert();
Matrix c_inv = c_denom.Invert();
System.Diagnostics.Debug.Assert((s_denom * s_inv).IsIdentity);
rpa[i].Xs = rpa[i].X0 * s_inv;
rpa[i].Xc = rpa[i].X0 * c_inv;
for (int l1 = 0; l1 < tb.Orbitals.Count; l1++)
{
for (int l2 = 0; l2 < tb.Orbitals.Count; l2++)
{
for (int l3 = 0; l3 < tb.Orbitals.Count; l3++)
{
for (int l4 = 0; l4 < tb.Orbitals.Count; l4++)
{
int a = GetIndex(tb, l1, l2);
int b = GetIndex(tb, l3, l4);
bool found = false;
if (rpa[i].Xs[a, b].MagnitudeSquared > largest)
{
largest = rpa[i].Xs[a, b].MagnitudeSquared;
charge = false;
found = true;
}
if (rpa[i].Xc[a, b].MagnitudeSquared > largest)
{
largest = rpa[i].Xc[a, b].MagnitudeSquared;
charge = true;
found = true;
}
if (found == false)
{
continue;
}
indices = string.Format("{0}{1}{2}{3}", l1, l2, l3, l4);
largestParams = rpa[i];
}
}
}
}
}
Output.WriteLine("Largest susceptibility found at:");
Output.WriteLine(" {0} susceptibility: {1}", charge ? "Charge" : "Spin", Math.Sqrt(largest));
Output.WriteLine(" Indices: {0}", indices);
Output.WriteLine(" Temperature: {0}", largestParams.Temperature);
Output.WriteLine(" Frequency: {0}", largestParams.Frequency);
Output.WriteLine(" Chemical Potential: {0}", largestParams.ChemicalPotential);
Output.WriteLine(" Q: {0}", largestParams.QptValue);
}
private static bool CenterOnGamma(Lattice lattice, ref KPoint qpt, KptList list)
{
double dist = qpt.Value.Magnitude;
double olddist = dist;
Vector3 newPt = qpt.Value;
bool retval = true;
double bs, bt;
list.GetPlaneST(qpt, out bs, out bt);
for (int k = -1; k <= 1; k++)
{
for (int j = -1; j <= 1; j++)
{
for (int i = -1; i <= 1; i++)
{
if (i == 0 && j == 0 && k == 0)
{
continue;
}
Vector3 pt = qpt.Value +
i * lattice.G1 +
j * lattice.G2 +
k * lattice.G3;
double s, t;
bool valid = list.GetPlaneST(new KPoint(pt), out s, out t);
if (!valid)
{
continue;
}
if (pt.Magnitude < dist - 1e-6)
{
if (list.allKpts.Any(x => Math.Abs((x.Value - pt).Magnitude) > 1e-6))
{
retval = false;
continue;
}
dist = pt.Magnitude;
newPt = pt;
}
}
}
}
if (olddist != dist)
{
retval = true;
}
if (retval == false)
{
return(false);
}
qpt.Value = newPt;
return(true);
}
public static KptList GenerateMesh(Lattice lattice, int[] kgrid, int[] shift, SymmetryList syms, bool includeEnds)
{
KptList retval = new KptList();
if (shift == null)
{
shift = new int[3];
}
for (int i = 0; i < 3; i++)
{
if (kgrid[i] == 1)
{
shift[i] = 1;
}
}
retval.mesh = (int[])kgrid.Clone();
retval.shift = (int[])shift.Clone();
retval.gammaCentered = true;
SymmetryList compatSyms = FindCompatibleSymmetries(kgrid, syms);
int index = 0;
for (int k = -kgrid[2] + shift[2]; k <= kgrid[2]; k += 2)
{
for (int j = -kgrid[1] + shift[1]; j <= kgrid[1]; j += 2)
{
for (int i = -kgrid[0] + shift[0]; i <= kgrid[0]; i += 2)
{
if (includeEnds == false)
{
if (k == kgrid[2])
{
break;
}
if (j == kgrid[1])
{
break;
}
if (i == kgrid[0])
{
break;
}
}
double dx = i * 0.5 / kgrid[0];
double dy = j * 0.5 / kgrid[1];
double dz = k * 0.5 / kgrid[2];
Vector3 kptValue = CalcK(lattice, dx, dy, dz);
int N = retval.KptToInteger(i, j, k);
int symN = N;
System.Diagnostics.Debug.Assert(!(retval.Nvalues.ContainsKey(N) && includeEnds == false));
List <int> orbitals = null;
bool foundSym = false;
foreach (var symmetry in compatSyms)
{
Vector3 Tpt = symmetry.Value * kptValue;
if (Tpt == kptValue)
{
continue;
}
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (Math.Abs(newi) % 2 != shift[0] ||
Math.Abs(newj) % 2 != shift[1] ||
Math.Abs(newk) % 2 != shift[2])
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (symN < N)
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
break;
}
}
if (includeEnds)
{
if (retval.AllNvalues.ContainsKey(N))
{
retval.allKpts.Add(new KPoint(kptValue));
continue;
}
}
retval.AllNvalues.Add(N, retval.allKpts.Count);
retval.allKpts.Add(new KPoint(kptValue));
if (foundSym == false)
{
retval.kpts.Add(new KPoint(kptValue));
retval.Nvalues.Add(N, index);
index++;
}
else
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].Weight++;
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
}
}
}
int count = kgrid[0] * kgrid[1] * kgrid[2];
for (int i = 0; i < retval.kpts.Count; i++)
{
retval.kpts[i].Weight /= count;
}
for (int i = 0; i < retval.allKpts.Count; i++)
{
retval.allKpts[i].Weight /= count;
}
return(retval);
}
private double FindMu(KptList ks, Matrix[] eigenvals, double Ntarget, double beta)
{
double N;
double mu_lower, mu_upper;
double N_lower, N_upper;
double mu;
mu_lower = mu_upper = mu = 0;
// first bracket
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
{
mu_upper = mu;
while (mu_lower >= mu_upper)
{
mu -= 1;
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
{
mu_upper = mu;
}
else
{
mu_lower = mu;
}
}
}
else
{
mu_lower = mu;
while (mu_lower >= mu_upper)
{
mu += 1;
N = FindNelec(ks, eigenvals, mu, beta);
if (N > Ntarget)
{
mu_upper = mu;
}
else
{
mu_lower = mu;
}
}
}
mu = 0.5 * (mu_upper + mu_lower);
N_lower = FindNelec(ks, eigenvals, mu_lower, beta);
N_upper = FindNelec(ks, eigenvals, mu_upper, beta);
// do linear extrapolation
int iter = 0;
while (Math.Abs(N - Ntarget) > 1e-11 && iter < 300)
{
double slope = (N_upper - N_lower) / (mu_upper - mu_lower);
if ((iter / 3) % 5 < 2)
{
// bisection in case system is gapped at target number
mu = 0.5 * (mu_upper + mu_lower);
}
else
{
// linear extrapoliation
mu = (Ntarget - N_lower) / slope + mu_lower;
}
N = FindNelec(ks, eigenvals, mu, beta);
if (N < Ntarget)
{
mu_lower = mu;
N_lower = N;
}
else if (N > Ntarget)
{
mu_upper = mu;
N_upper = N;
}
iter++;
}
if (iter >= 300)
{
Output.WriteLine("Failed to find chemical potential. Check the number of electrons.");
throw new Exception("Failed to find chemical potential.");
}
return(mu);
}
private RpaThreadInfo[] CreateThreadInfos(TightBinding tb, List <RpaParams> rpa, KptList qpts)
{
RpaThreadInfo[] infos = new RpaThreadInfo[threads];
for (int i = 0; i < infos.Length; i++)
{
infos[i] = new RpaThreadInfo();
infos[i].tb = tb.Clone();
infos[i].qpts = qpts;
}
infos[0].PrimaryThread = true;
for (int i = 0; i < rpa.Count; i++)
{
infos[i % threads].RpaParams.Add(rpa[i]);
}
return(infos);
}
void DoDensityOfStates()
{
KptList ks = KMesh;
using (StreamWriter outf = new StreamWriter(outputfile + ".dos"))
{
double smearing = TemperatureMesh[0];
double effBeta = 1 / smearing;
double emin = double.MaxValue, emax = double.MinValue;
for (int i = 0; i < ks.Kpts.Count; i++)
{
KPoint kpt = ks.Kpts[i];
emin = Math.Min(emin, kpt.Wavefunctions.Min(x => x.Energy));
emax = Math.Max(emax, kpt.Wavefunctions.Max(x => x.Energy));
}
emin -= smearing * 10;
emax += smearing * 10;
emin -= MuMesh[0];
emax -= MuMesh[0];
int epts = 3000;
double[] energyGrid = new double[epts];
double[,] dos = new double[epts, Orbitals.Count + 1];
int zeroIndex = 0;
Output.WriteLine(
"Calculating DOS from {0} to {1} with finite temperature smearing {2}.",
emin, emax, smearing);
Output.WriteLine("Using {0} kpts.", ks.Kpts.Count);
for (int i = 0; i < epts; i++)
{
energyGrid[i] = emin + (emax - emin) * i / (double)(epts - 1);
if (energyGrid[i] < 0)
{
zeroIndex = i;
}
}
for (int i = 0; i < ks.Kpts.Count; i++)
{
KPoint kpt = ks.Kpts[i];
for (int j = 0; j < kpt.Wavefunctions.Count; j++)
{
Wavefunction wfk = kpt.Wavefunctions[j];
double energy = wfk.Energy - MuMesh[0];
int startIndex = FindIndex(energyGrid, energy - smearing * 10);
int endIndex = FindIndex(energyGrid, energy + smearing * 10);
for (int k = startIndex; k <= endIndex; k++)
{
double ferm = FermiFunction(energyGrid[k], energy, effBeta);
double smearWeight = ferm * (1 - ferm) * effBeta;
smearWeight *= ks.Kpts[i].Weight;
double weight = 0;
for (int l = 0; l < wfk.Coeffs.Length; l++)
{
if (PoleStates.Contains(l))
{
continue;
}
double stateval = wfk.Coeffs[l].MagnitudeSquared;
weight += stateval;
}
if (PoleStates.Count == 0 && Math.Abs(weight - 1) > 1e-8)
{
throw new Exception("Eigenvector not normalized!");
}
dos[k, 0] += smearWeight * weight;
for (int state = 0; state < wfk.Coeffs.Length; state++)
{
if (PoleStates.Contains(state))
{
continue;
}
double wtk = wfk.Coeffs[state].MagnitudeSquared;
dos[k, state + 1] += smearWeight * wtk;
}
}
}
}
// symmetrize DOS for equivalent orbitals.
for (int k = 0; k < epts; k++)
{
for (int i = 0; i < Orbitals.Count; i++)
{
double wtk = dos[k, i + 1];
int count = 1;
foreach (int equiv in Orbitals[i].Equivalent)
{
wtk += dos[k, equiv + 1];
count++;
}
dos[k, i + 1] = wtk / count;
foreach (int equiv in Orbitals[i].Equivalent)
{
dos[k, equiv + 1] = wtk / count;
}
}
}
if (emin < 0 && emax > 0)
{
if (zeroIndex + 1 >= energyGrid.Length)
{
zeroIndex = energyGrid.Length - 2;
}
double slope = (dos[zeroIndex, 0] - dos[zeroIndex + 1, 0]) / (energyGrid[zeroIndex] - energyGrid[zeroIndex + 1]);
double dosEF = slope * (-energyGrid[zeroIndex]) + dos[zeroIndex, 0];
Output.WriteLine("Density of states at chemical potential: {0}", dosEF);
for (int i = 0; i < epts; i++)
{
outf.Write("{0} ", energyGrid[i]);
for (int j = 0; j < Orbitals.Count + 1; j++)
{
outf.Write("{0} ", dos[i, j]);
}
outf.WriteLine();
}
}
}
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptList retval = new KptList();
retval.mesh = (int[])qmesh.mesh.Clone();
retval.shift = new int[3];
retval.gammaCentered = true;
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = Vector3.CrossProduct(norm, diff_1);
NormalizeST(lattice, retval);
int zmax = qmesh.mesh[2] * 2;
int ymax = qmesh.mesh[1] * 2;
int xmax = qmesh.mesh[0] * 2;
int index = 0;
List <KPoint> planePoints = new List <KPoint>();
for (int i = 0; i < qmesh.AllKpts.Count; i++)
{
var qpt = qmesh.AllKpts[i];
Vector3 diff = qpt.Value - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
planePoints.Add(qpt);
}
}
SortByDistanceFromGamma(planePoints);
for (int i = 0; i < planePoints.Count; i++)
{
var qpt = planePoints[i];
double s, t;
retval.GetPlaneST(qpt, out s, out t);
//if (CenterOnGamma(lattice, ref qpt, retval) == false)
// continue;
//retval.GetPlaneST(qpt, out news, out newt);
retval.allKpts.Add(qpt);
}
// now sort q-points to lay them in the s,t plane.
Comparison <KPoint> sorter = (x, y) =>
{
double s_x, s_y, t_x, t_y;
retval.GetPlaneST(x, out s_x, out t_x);
retval.GetPlaneST(y, out s_y, out t_y);
if (Math.Abs(t_x - t_y) > 1e-6)
{
return(t_x.CompareTo(t_y));
}
else
{
return(s_x.CompareTo(s_y));
}
};
retval.allKpts.Sort(sorter);
// now reduce points by symmetry.
for (int i = 0; i < retval.allKpts.Count; i++)
{
var qpt = retval.AllKpts[i];
int N = retval.KptToInteger(lattice, qpt);
int symN = N;
bool foundSym = false;
List <int> orbitals = null;
Vector3 pt = qpt.Value;
foreach (var symmetry in syms)
{
Vector3 Tpt = symmetry.Value * pt;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
{
continue;
}
symN = retval.KptToInteger(newi, newj, newk);
if (retval.Nvalues.ContainsKey(symN))
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
{
break;
}
}
if (foundSym == false && retval.Nvalues.ContainsKey(N) == false)
{
retval.kpts.Add(qpt);
retval.Nvalues.Add(N, index);
index++;
}
else if (retval.Nvalues.ContainsKey(N) == false)
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
else
{
} // skip points which are already in there. This should only happen for zone edge points
}
retval.kpts.Sort(sorter);
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return(retval);
}
/// <summary>
/// This function does not work with symmetries, so it is unused.
/// </summary>
/// <param name="inp"></param>
/// <param name="outputfile"></param>
void tet_DoDensityOfStates(TightBinding.TbInputFileReader inp)
{
KptList ks = KMesh;
StreamWriter outf = new StreamWriter(outputfile + ".dos");
double smearing = TemperatureMesh[0];
double smearNorm = 1 / smearing * Math.Pow(Math.PI, -0.5);
double oneOverSmearSquared = Math.Pow(smearing, -2);
double emin, emax;
Hoppings.EnergyScale(out emin, out emax);
emin -= smearing * 5;
emax += smearing * 5;
int epts = 2000;
double[] energyGrid = new double[epts];
double[,] dos = new double[epts, Orbitals.Count + 1];
smearNorm /= ks.Kpts.Count;
for (int i = 0; i < epts; i++)
{
energyGrid[i] = emin + (emax - emin) * i / (double)(epts - 1);
}
Output.WriteLine("Calculating DOS from {0} to {1} with tetrahedron method.",
emin, emax, smearing);
Output.WriteLine("Using {0} tetrahedrons.", ks.Tetrahedrons.Count);
for (int tetindex = 0; tetindex < ks.Tetrahedrons.Count; tetindex++)
{
Tetrahedron tet = ks.Tetrahedrons[tetindex];
if (tetindex % (ks.Tetrahedrons.Count / 10) == 0 && tetindex > 0)
{
Output.WriteLine("At {0}...", tetindex);
}
Matrix[] eigenvals = new Matrix[4];
for (int i = 0; i < 4; i++)
{
Matrix m = CalcHamiltonian(tet.Corners[i]);
Matrix vals, vecs;
m.EigenValsVecs(out vals, out vecs);
eigenvals[i] = vals;
}
for (int nband = 0; nband < eigenvals[0].Rows; nband++)
{
for (int i = 0; i < 4; i++)
{
tet.Values[i] = eigenvals[i][nband, 0].RealPart;
}
tet.SortCorners();
int estart = FindIndex(energyGrid, tet.Values[0]);
int eend = FindIndex(energyGrid, tet.Values[3]);
for (int ei = estart; ei < eend; ei++)
{
dos[ei, 0] += tet.IntegrateArea(energyGrid[ei]);
}
}
}
for (int i = 0; i < epts; i++)
{
dos[i, 0] /= ks.Tetrahedrons.Count;
}
for (int i = 0; i < epts; i++)
{
outf.Write("{0} ", energyGrid[i]);
for (int j = 0; j < Orbitals.Count + 1; j++)
{
outf.Write("{0} ", dos[i, j]);
}
outf.WriteLine();
}
outf.Close();
Output.WriteLine("Creating +coeff file.");
outf = new StreamWriter(Path.Combine(Path.GetDirectoryName(outputfile), "+coeff"));
outf.WriteLine("#\t1\t0\t" + ks.Kpts.Count.ToString());
outf.Write("# band index\te(k,n)\t");
for (int i = 0; i < Orbitals.Count; i++)
{
if (string.IsNullOrEmpty(Orbitals[i].Name))
{
outf.Write("TB{0}\t", i);
}
else
{
outf.Write("{0}\t", Orbitals[i].Name);
}
}
outf.WriteLine();
for (int kindex = 0; kindex < ks.Kpts.Count; kindex++)
{
Matrix m = CalcHamiltonian(ks.Kpts[kindex]);
Matrix vals, vecs;
m.EigenValsVecs(out vals, out vecs);
outf.WriteLine("# spin= 1 k={0}", ks.Kpts[kindex].Value);
for (int i = 0; i < vals.Rows; i++)
{
outf.Write("{0} {1} ", i + 1, vals[i, 0].RealPart);
for (int j = 0; j < vecs.Columns; j++)
{
outf.Write("{0} {1} ", vecs[i, j].RealPart, vecs[i, j].ImagPart);
}
outf.WriteLine();
}
}
}
private void CalcSusceptibility(TightBinding tb, KptList qpts, List<RpaParams> rpa)
{
Matrix ident = Matrix.Identity(tb.Orbitals.Count * tb.Orbitals.Count);
Matrix[] S, C;
CalcSpinChargeMatrices(tb, rpa, out S, out C);
Output.WriteLine("Calculating X0...");
RpaThreadInfo[] threadInfos = CreateThreadInfos(tb, rpa, qpts);
Output.WriteLine("Using {0} threads.", threads);
for (int i = 0; i < threadInfos.Length; i++)
{
RunRpaThread(threadInfos[i]);
if (i == 0)
Thread.Sleep(20);
}
bool threadsRunning;
do
{
threadsRunning = false;
for (int i = 0; i < threadInfos.Length; i++)
{
if (threadInfos[i].Thread.ThreadState == ThreadState.Running)
threadsRunning = true;
}
Thread.Sleep(10);
} while (threadsRunning);
Output.WriteLine();
Output.WriteLine("Bare susceptibility calculation completed.");
Output.WriteLine();
double factor = InteractionAdjustment(rpa, S, C, tb);
if (tb.Interactions.AdjustInteractions)
{
Output.WriteLine("Multiplying interactions by {0}.", factor);
for (int i = 0; i < rpa.Count; i++)
{
S[i] *= factor;
C[i] *= factor;
}
}
else if (factor < 1)
{
Output.WriteLine("WARNING: There will be divergent geometric series.");
Output.WriteLine(" Interpret results with care!");
}
Output.WriteLine();
Output.WriteLine("Calculating dressed susceptibilities.");
Output.WriteLine();
RpaParams largestParams = null;
double largest = 0;
string indices = "";
bool charge = false;
for (int i = 0; i < rpa.Count; i++)
{
Matrix s_denom = (ident - S[i] * rpa[i].X0);
Matrix c_denom = (ident + C[i] * rpa[i].X0);
Matrix s_inv = s_denom.Invert();
Matrix c_inv = c_denom.Invert();
System.Diagnostics.Debug.Assert((s_denom * s_inv).IsIdentity);
rpa[i].Xs = rpa[i].X0 * s_inv;
rpa[i].Xc = rpa[i].X0 * c_inv;
for (int l1 = 0; l1 < tb.Orbitals.Count; l1++)
{
for (int l2 = 0; l2 < tb.Orbitals.Count; l2++)
{
for (int l3 = 0; l3 < tb.Orbitals.Count; l3++)
{
for (int l4 = 0; l4 < tb.Orbitals.Count; l4++)
{
int a = GetIndex(tb, l1, l2);
int b = GetIndex(tb, l3, l4);
bool found = false;
if (rpa[i].Xs[a,b].MagnitudeSquared > largest)
{
largest = rpa[i].Xs[a,b].MagnitudeSquared;
charge = false;
found = true;
}
if (rpa[i].Xc[a, b].MagnitudeSquared > largest)
{
largest = rpa[i].Xc[a, b].MagnitudeSquared;
charge = true;
found = true;
}
if (found == false)
continue;
indices = string.Format("{0}{1}{2}{3}", l1, l2, l3, l4);
largestParams = rpa[i];
}
}
}
}
}
Output.WriteLine("Largest susceptibility found at:");
Output.WriteLine(" {0} susceptibility: {1}", charge ? "Charge" : "Spin", Math.Sqrt(largest));
Output.WriteLine(" Indices: {0}", indices);
Output.WriteLine(" Temperature: {0}", largestParams.Temperature);
Output.WriteLine(" Frequency: {0}", largestParams.Frequency);
Output.WriteLine(" Chemical Potential: {0}", largestParams.ChemicalPotential);
Output.WriteLine(" Q: {0}", largestParams.QptValue);
}
private double FindNelec(KptList ks, Matrix[] eigenvals, double mu, double beta)
{
double N = 0;
for (int i = 0; i < ks.Kpts.Count; i++)
{
double weight = ks.Kpts[i].Weight;
for (int j = 0; j < eigenvals[i].Rows; j++)
{
double energy = eigenvals[i][j, 0].RealPart;
double npt = 2 * FermiFunction(energy, mu, beta);
N += npt * weight;
}
}
return N;
}
private RpaThreadInfo[] CreateThreadInfos(TightBinding tb, List<RpaParams> rpa, KptList qpts)
{
RpaThreadInfo[] infos = new RpaThreadInfo[threads];
for (int i = 0; i < infos.Length; i++)
{
infos[i] = new RpaThreadInfo();
infos[i].tb = tb.Clone();
infos[i].qpts = qpts;
}
infos[0].PrimaryThread = true;
for (int i = 0; i < rpa.Count; i++)
{
infos[i % threads].RpaParams.Add(rpa[i]);
}
return infos;
}
protected override void Validate()
{
if (tb.lattice == null)
{
ThrowEx(@"""Lattice"" section missing.");
}
if (tb.sites == null)
{
ThrowEx(@"""Sites"" section missing.");
}
if (tb.hoppings == null)
{
ThrowEx(@"""Hoppings"" section missing.");
}
if (tb.kpath == null)
{
tb.kpath = KptList.DefaultPath(tb.lattice);
}
if (tb.kgrid == null || tb.kgrid[0] == 0 || tb.kgrid[1] == 0 || tb.kgrid[2] == 0)
{
ThrowEx(@"KMesh was not defined properly.");
}
if (tb.sites.Count == 0)
{
ThrowEx(@"There are no sites.");
}
if (tb.hoppings.Count == 0)
{
ThrowEx(@"There are no hoppings.");
}
if (tb.symmetries.Count == 0)
{
tb.symmetries.Add(new Symmetry(Matrix.Identity(3)));
}
if (tb.Nelec != null)
{
if (tb.MuMesh != null)
{
ThrowEx(@"Specify only one of Nelec or Mu.");
}
tb.MuMesh = new double[tb.Nelec.Length];
for (int i = 0; i < tb.Nelec.Length; i++)
{
if (tb.Nelec[i] > tb.Orbitals.Count * 2)
{
ThrowEx(@"Nelec is too large.");
}
else if (tb.Nelec[i] < 0)
{
ThrowEx(@"Nelec cannot be less than zero.");
}
}
}
if (tb.MuMesh == null)
{
tb.MuMesh = new double[] { 0 }
}
;
if (tb.TemperatureMesh == null)
{
tb.TemperatureMesh = new double[] { 1 }
}
;
if (tb.FrequencyMesh == null)
{
tb.FrequencyMesh = new double[] { 0 }
}
;
foreach (HoppingPair h in tb.hoppings)
{
if (h.Left >= tb.sites.Count || h.Right >= tb.sites.Count)
{
ThrowEx(string.Format(@"The hopping {0} to {1} was specified, but there are only {2} sites.",
h.Left + 1, h.Right + 1, tb.sites.Count));
}
}
foreach (Orbital orb in tb.Orbitals)
{
var interactionOrbs = tb.Orbitals.Where((x, y) => x.InteractionGroup == orb.InteractionGroup);
foreach (Orbital otherOrb in interactionOrbs)
{
Vector3 delta = otherOrb.Location - orb.Location;
if (delta.Magnitude > 1e-8)
{
ThrowEx(string.Format("In the interaction group {0}, orbitals {1} and {2} are present, but they are in different positions.",
orb.InteractionGroup, orb.Name, otherOrb.Name));
}
}
}
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, int[] qgrid, int[] qshift)
{
KptList qmesh = GenerateMesh(lattice, qgrid, qshift, syms, true);
return(GeneratePlane(lattice, points, syms, qmesh));
}
public KptList Clone()
{
KptList retval = new KptList();
retval.allKpts.AddRange(allKpts.Select(x => x.Clone()));
retval.kpts.AddRange(kpts.Select(x => x.Clone()));
if (mesh != null)
retval.mesh = (int[])mesh.Clone();
if (shift != null)
retval.shift = (int[])shift.Clone();
retval.gammaCentered = gammaCentered;
foreach (KeyValuePair<int, int> var in Nvalues)
retval.Nvalues.Add(var.Key, var.Value);
foreach (KeyValuePair<int, int> var in AllNvalues)
retval.AllNvalues.Add(var.Key, var.Value);
retval.sdir = sdir;
retval.tdir = tdir;
retval.origin = origin;
return retval;
}
public static KptList GeneratePlane(Lattice lattice, Vector3[] points, SymmetryList syms, KptList qmesh)
{
Vector3 diff_1 = points[1] - points[0];
Vector3 diff_2 = points[2] - points[0];
Vector3 norm = Vector3.CrossProduct(diff_1, diff_2);
KptList retval = new KptList();
retval.mesh = (int[])qmesh.mesh.Clone();
retval.shift = new int[3];
retval.gammaCentered = true;
retval.origin = points[0];
retval.sdir = diff_1;
retval.tdir = Vector3.CrossProduct(norm, diff_1);
NormalizeST(lattice, retval);
int zmax = qmesh.mesh[2] * 2;
int ymax = qmesh.mesh[1] * 2;
int xmax = qmesh.mesh[0] * 2;
int index = 0;
List<KPoint> planePoints = new List<KPoint>();
for (int i = 0; i < qmesh.AllKpts.Count; i++)
{
var qpt = qmesh.AllKpts[i];
Vector3 diff = qpt.Value - points[0];
double dot = Math.Abs(diff.DotProduct(norm));
if (dot < 1e-8)
{
double s, t;
retval.GetPlaneST(qpt, out s, out t);
planePoints.Add(qpt);
}
}
SortByDistanceFromGamma(planePoints);
for (int i = 0; i <planePoints.Count; i++)
{
var qpt = planePoints[i];
double s, t;
retval.GetPlaneST(qpt, out s, out t);
//if (CenterOnGamma(lattice, ref qpt, retval) == false)
// continue;
//retval.GetPlaneST(qpt, out news, out newt);
retval.allKpts.Add(qpt);
}
// now sort q-points to lay them in the s,t plane.
Comparison<KPoint> sorter = (x, y) =>
{
double s_x, s_y, t_x, t_y;
retval.GetPlaneST(x, out s_x, out t_x);
retval.GetPlaneST(y, out s_y, out t_y);
if (Math.Abs(t_x - t_y) > 1e-6)
return t_x.CompareTo(t_y);
else
return s_x.CompareTo(s_y);
};
retval.allKpts.Sort(sorter);
// now reduce points by symmetry.
for (int i = 0; i < retval.allKpts.Count; i++)
{
var qpt = retval.AllKpts[i];
int N = retval.KptToInteger(lattice, qpt);
int symN = N;
bool foundSym = false;
List<int> orbitals = null;
Vector3 pt = qpt.Value;
foreach (var symmetry in syms)
{
Vector3 Tpt = symmetry.Value * pt;
int newi, newj, newk;
retval.ReduceKpt(lattice, Tpt, out newi, out newj, out newk);
if (newi % 2 != 0 || newj % 2 != 0 || newk % 2 != 0)
continue;
symN = retval.KptToInteger(newi, newj, newk);
if (retval.Nvalues.ContainsKey(symN))
{
foundSym = true;
if (symmetry.OrbitalTransform.Count > 0)
{
orbitals = symmetry.OrbitalTransform;
}
}
if (foundSym)
break;
}
if (foundSym == false && retval.Nvalues.ContainsKey(N) == false)
{
retval.kpts.Add(qpt);
retval.Nvalues.Add(N, index);
index++;
}
else if (retval.Nvalues.ContainsKey(N) == false)
{
int newIndex = retval.Nvalues[symN];
retval.kpts[newIndex].AddOrbitalSymmetry(orbitals);
retval.Nvalues.Add(N, newIndex);
}
else
{ } // skip points which are already in there. This should only happen for zone edge points
}
retval.kpts.Sort(sorter);
Vector3 sd = retval.sdir / SmallestNonzero(retval.sdir);
Vector3 td = retval.tdir / SmallestNonzero(retval.tdir);
Output.WriteLine("Plane horizontal direction: {0}", sd);
Output.WriteLine("Plane vertical direction: {0}", td);
Output.WriteLine("Plane horizontal vector: {0}", retval.sdir);
Output.WriteLine("Plane vertical vector: {0}", retval.tdir);
return retval;
}
