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 static int Main(string[] args)
{
using (BootStrap b = new BootStrap())
{
System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
watch.Start();
string filename = b.GetInputFile("Tight Binding code", "tb", args);
TightBinding c = new TightBinding();
c.LoadTB(filename);
c.RunTB();
watch.Stop();
Output.WriteLine("Total time: {0} s", watch.ElapsedMilliseconds / 1000.0);
long milliseconds = watch.ElapsedMilliseconds;
int seconds = (int)(milliseconds / 1000L);
int minutes = seconds / 60;
int hours = minutes / 60;
minutes %= 60;
seconds %= 60;
milliseconds %= 1000;
Output.WriteLine(" {0}:{1:00}:{2:00}.{3:000}", hours, minutes, seconds, milliseconds);
return 0;
}
}
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 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 List<RpaParams> CreateRpaParameterList(TightBinding tb, List<KPoint> QMesh)
{
double[] FrequencyMesh = tb.FrequencyMesh;
double[] TemperatureMesh = tb.TemperatureMesh;
List<RpaParams> rpa = new List<RpaParams>();
for (int tempIndex = 0; tempIndex < TemperatureMesh.Length; tempIndex++)
{
for (int muIndex = 0; muIndex < tb.MuMesh.Length; muIndex++)
{
for (int qIndex = 0; qIndex < QMesh.Count; qIndex++)
{
for (int freqIndex = 0; freqIndex < FrequencyMesh.Length; freqIndex++)
{
rpa.Add(new RpaParams(
qIndex,
QMesh[qIndex].Value,
TemperatureMesh[tempIndex],
FrequencyMesh[freqIndex],
tb.MuMesh[muIndex]));
}
}
}
}
return rpa;
}
public static int Main(string[] args)
{
using (BootStrap b = new BootStrap())
{
System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
watch.Start();
string filename = b.GetInputFile("Tight Binding code", "tb", args);
TightBinding c = new TightBinding();
c.LoadTB(filename);
c.RunTB();
watch.Stop();
Output.WriteLine("Total time: {0} s", watch.ElapsedMilliseconds / 1000.0);
long milliseconds = watch.ElapsedMilliseconds;
int seconds = (int)(milliseconds / 1000L);
int minutes = seconds / 60;
int hours = minutes / 60;
minutes %= 60;
seconds %= 60;
milliseconds %= 1000;
Output.WriteLine(" {0}:{1:00}:{2:00}.{3:000}", hours, minutes, seconds, milliseconds);
return(0);
}
}
void Run(TightBinding tb, List <string> args)
{
foreach (var arg in args)
{
Console.WriteLine("Reading file " + arg);
CreateBands(tb, arg);
}
}
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);
}
}
}
private void SaveMatricesQPlane(TightBinding tb, List <KPoint> QMesh, List <RpaParams> chi, MatrixGetter g, string name)
{
if (tb.TemperatureMesh.Length > 1)
{
Directory.CreateDirectory("temperature");
SaveByTemperature(tb, QMesh, chi, g, name);
}
SaveByQPlane(tb, QMesh, chi, g, name);
}
double CalcDistance(TightBinding tb, Vector3 v1, Vector3 v2)
{
Vector3 delta = v1 - v2;
ShiftDelta(ref delta, tb.Lattice.G1);
ShiftDelta(ref delta, tb.Lattice.G2);
ShiftDelta(ref delta, tb.Lattice.G3);
return(delta.Magnitude);
}
double CalcDistance(TightBinding tb, Vector3 v1, Vector3 v2)
{
Vector3 delta = v1 - v2;
ShiftDelta(ref delta, tb.Lattice.G1);
ShiftDelta(ref delta, tb.Lattice.G2);
ShiftDelta(ref delta, tb.Lattice.G3);
return delta.Magnitude;
}
private void VerifySymmetry(TightBinding tb, Matrix S, int a, int b)
{
for (int m1 = 0; m1 < 2; m1++)
{
for (int m2 = 0; m2 < 2; m2++)
{
for (int m3 = 0; m3 < 2; m3++)
{
for (int m4 = 0; m4 < 2; m4++)
{
int l1 = Select(m1, a, b);
int l2 = Select(m2, a, b);
int l3 = Select(m3, a, b);
int l4 = Select(m4, a, b);
int a1 = Select(m1, b, a);
int a2 = Select(m2, b, a);
int a3 = Select(m3, b, a);
int a4 = Select(m4, b, a);
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
int ii = GetIndex(tb, a1, a2);
int jj = GetIndex(tb, a3, a4);
var diff = S[i, j] - S[ii, jj];
if (diff.Magnitude > 1e-8)
{
Output.WriteLine("ERROR: Failed to verify symmetry.");
Output.WriteLine(" a = {0} b = {1}", a, b);
Output.WriteLine(" L = {0}{1}{2}{3}", l1, l2, l3, l4);
Output.WriteLine(" A = {0}{1}{2}{3}", a1, a2, a3, a4);
Output.WriteLine(" ij = {0},{1} {2},{3}", i, j, ii, jj);
Output.WriteLine(" M[i,j] = {0} {1}", S[i, j], S[ii, jj]);
Output.WriteLine(" diff = {0}", diff.Magnitude);
try
{
throw new Exception("blah");
}
catch (Exception e)
{
Output.WriteLine(e.StackTrace);
}
Environment.Exit(4);
}
}
}
}
}
}
double InteractionAdjustment(List <RpaParams> rpa, Matrix[] S, Matrix[] C, TightBinding tb)
{
double largest = double.MinValue;
RpaParams largestParams = null;
bool Cdiv = false;
for (int i = 0; i < rpa.Count; i++)
{
RpaParams p = rpa[i];
Matrix x0 = p.X0;
double lv = LargestPositiveEigenvalue(x0 * S[i]);
if (lv > largest)
{
largest = lv;
largestParams = p;
Cdiv = false;
}
lv = LargestPositiveEigenvalue(-x0 * C[i]);
if (lv > largest)
{
largest = lv;
largestParams = p;
Cdiv = true;
}
}
if (largest >= 1)
{
Output.WriteLine("Interaction should be reduced to avoid divergence.", largest);
}
Output.WriteLine("Largest eigenvalue of denominator found at:");
Output.WriteLine(" Eigenvalue: {0}", largest);
Output.WriteLine(" {0} susceptibility", Cdiv ? "Charge" : "Spin");
Output.WriteLine(" q = {0}", largestParams.QptValue);
Output.WriteLine(" Temperature = {0}", largestParams.Temperature);
Output.WriteLine(" Chemical Potential = {0}", largestParams.ChemicalPotential);
Output.WriteLine(" Frequency = {0}", largestParams.Frequency);
largest /= tb.Interactions.MaxEigenvalue;
Output.WriteLine();
return(1 / largest);
}
static void Main(string[] args)
{
using (BootStrap b = new BootStrap())
{
string inputfile = b.GetInputFile("RPA Analysis code", "rpanal", args);
TightBinding tb = new TightBinding(inputfile);
RPA inst = new RPA();
Vector3 q = GetQpoint();
List<KPoint> qpt = new List<KPoint>();
qpt.Add(new KPoint(q));
var parameters = inst.CreateRpaParameterList(tb, qpt);
}
}
static void Main(string[] args)
{
using (BootStrap b = new BootStrap())
{
string inputfile = b.GetInputFile("RPA Analysis code", "rpanal", args);
TightBinding tb = new TightBinding(inputfile);
RPA inst = new RPA();
Vector3 q = GetQpoint();
List <KPoint> qpt = new List <KPoint>();
qpt.Add(new KPoint(q));
var parameters = inst.CreateRpaParameterList(tb, qpt);
}
}
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();
}
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);
}
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");
}
}
public static void Main(string[] args)
{
Directory.SetCurrentDirectory("/home/eylvisaker/Calculations/rpa/tests");
using (BootStrap b = new BootStrap())
{
if (args.Length == 0)
{
Console.WriteLine("Must specify tight binding input and eigenvalues files on command line.");
System.Environment.Exit(1);
}
string inputfile = b.GetInputFile("Band Path code", "bandpath", args);
TightBinding tb = new TightBinding(inputfile);
var argsList = args.ToList();
argsList.RemoveAt(0);
new BandPath().Run(tb, argsList);
}
}
public static void Main(string[] args)
{
Directory.SetCurrentDirectory("/home/eylvisaker/Calculations/rpa/tests");
using (BootStrap b = new BootStrap())
{
if (args.Length == 0)
{
Console.WriteLine("Must specify tight binding input and eigenvalues files on command line.");
System.Environment.Exit(1);
}
string inputfile = b.GetInputFile("Band Path code", "bandpath", args);
TightBinding tb = new TightBinding(inputfile);
var argsList = args.ToList();
argsList.RemoveAt(0);
new BandPath().Run(tb, argsList);
}
}
private void CalcOnSiteInteraction(TightBinding tb, Matrix _S, Matrix _C, InteractionPair interaction)
{
foreach (int l1 in interaction.OrbitalsLeft)
{
foreach (int l2 in interaction.OrbitalsLeft)
{
foreach (int l3 in interaction.OrbitalsRight)
{
foreach (int l4 in interaction.OrbitalsRight)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
if (l1 == l2 && l2 == l3 && l3 == l4)
{
_S[i, j] += interaction.HubbardU;
_C[i, j] += interaction.HubbardU;
}
else if (l1 == l4 && l4 != l2 && l2 == l3)
{
_S[i, j] += interaction.InterorbitalU;
_C[i, j] += (-interaction.InterorbitalU + interaction.Exchange);
}
else if (l1 == l2 && l2 != l3 && l3 == l4)
{
_S[i, j] += interaction.Exchange;
_C[i, j] += 2 * interaction.InterorbitalU - interaction.Exchange;
}
else if (l1 == l3 && l3 != l2 && l2 == l4)
{
_S[i, j] += interaction.PairHopping;
_C[i, j] += interaction.PairHopping;
}
}
}
}
}
}
public TightBinding Clone()
{
TightBinding retval = new TightBinding();
retval.lattice = lattice.Clone();
retval.sites = sites.Clone();
retval.hoppings = hoppings.Clone();
retval.kpath = kpath.Clone();
retval.kmesh = kmesh.Clone();
if (qmesh != null)
{
retval.qmesh = qmesh.Clone();
}
if (qplane != null)
{
retval.qplane = qplane.Clone();
}
retval.poles.AddRange(poles);
retval.FrequencyMesh = (double[])FrequencyMesh.Clone();
retval.TemperatureMesh = (double[])TemperatureMesh.Clone();
retval.MuMesh = (double[])MuMesh.Clone();
retval.Nelec = (double[])Nelec.Clone();
retval.Interactions = Interactions.Clone();
retval.kgrid = (int[])kgrid.Clone();
retval.kshift = (int[])kshift.Clone();
retval.symmetries = symmetries.Clone();
retval.qgrid = (int[])qgrid.Clone();
retval.qshift = (int[])qshift.Clone();
retval.qplaneDef = (Vector3[])qplaneDef.Clone();
retval.setQplane = setQplane;
retval.specifiedNelec = specifiedNelec;
retval.outputfile = outputfile;
return(retval);
}
private void SaveByTemperature(TightBinding tb, List <KPoint> QMesh, List <RpaParams> rpa, MatrixGetter g, string name)
{
rpa.Sort(RpaParams.TemperatureComparison);
Complex[] chisum = new Complex[rpa.Count];
double[] chimag = new double[rpa.Count];
double[] chimagsqr = new double[rpa.Count];
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 i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
// organize by temperature
string filename = string.Format(
"temperature/{0}.{1}{2}{3}{4}.T", name, l1, l2, l3, l4);
double lastFreq = double.MinValue;
double lastMu = double.MinValue;
double lastq = int.MinValue;
using (StreamWriter w = new StreamWriter(filename))
{
for (int index = 0; index < rpa.Count; index++)
{
bool newline = false;
newline |= ChangeValue(ref lastFreq, rpa[index].Frequency);
newline |= ChangeValue(ref lastMu, rpa[index].ChemicalPotential);
newline |= ChangeValue(ref lastq, rpa[index].Qindex);
if (newline)
{
w.WriteLine();
w.WriteLine("# Frequency: {0}", rpa[index].Frequency);
w.WriteLine("# Chemical Potential: {0}", rpa[index].ChemicalPotential);
w.WriteLine("# Q: {0}", QMesh[rpa[index].Qindex]);
w.WriteLine("#");
w.WriteLine("# Temperature\tRe(Chi)\tIm(Chi)");
}
Complex val = g(rpa[index])[i, j];
chisum[index] += val;
chimag[index] += val.Magnitude;
chimagsqr[index] += val.MagnitudeSquared;
w.WriteLine("\t{0:0.000000}\t{1:0.0000000}\t{2:0.0000000}",
rpa[index].Temperature, val.RealPart, val.ImagPart);
}
}
}
}
}
}
}
public TightBinding Clone()
{
TightBinding retval = new TightBinding();
retval.lattice = lattice.Clone();
retval.sites = sites.Clone();
retval.hoppings = hoppings.Clone();
retval.kpath = kpath.Clone();
retval.kmesh = kmesh.Clone();
if (qmesh != null) retval.qmesh = qmesh.Clone();
if (qplane != null) retval.qplane = qplane.Clone();
retval.poles.AddRange(poles);
retval.FrequencyMesh = (double[])FrequencyMesh.Clone();
retval.TemperatureMesh = (double[])TemperatureMesh.Clone();
retval.MuMesh = (double[])MuMesh.Clone();
retval.Nelec = (double[])Nelec.Clone();
retval.Interactions = Interactions.Clone();
retval.kgrid = (int[])kgrid.Clone();
retval.kshift = (int[])kshift.Clone();
retval.symmetries = symmetries.Clone();
retval.qgrid = (int[])qgrid.Clone();
retval.qshift = (int[])qshift.Clone();
retval.qplaneDef = (Vector3[])qplaneDef.Clone();
retval.setQplane = setQplane;
retval.specifiedNelec = specifiedNelec;
retval.outputfile = outputfile;
return retval;
}
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 Run(TightBinding tb, List<string> args)
{
foreach(var arg in args)
{
Console.WriteLine("Reading file " + arg);
CreateBands(tb, arg);
}
}
private void SaveMatricesQPlane(TightBinding tb, List<KPoint> QMesh, List<RpaParams> chi, MatrixGetter g, string name)
{
if (tb.TemperatureMesh.Length > 1)
{
Directory.CreateDirectory("temperature");
SaveByTemperature(tb, QMesh, chi, g, name);
}
SaveByQPlane(tb, QMesh, chi, g, name);
}
private void SaveByQPlane(TightBinding tb, List<KPoint> QMesh, List<RpaParams> rpa, MatrixGetter g, string name)
{
rpa.Sort(RpaParams.QIndexComparison);
Complex[] chisum = new Complex[rpa.Count];
double[] chimag = new double[rpa.Count];
double[] chimagsqr = new double[rpa.Count];
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++)
{
double lastFreq = double.MinValue;
double lastMu = double.MinValue;
double lastq = int.MinValue;
int baseIndex = 0;
for (int ti = 0; ti < tb.TemperatureMesh.Length; ti++)
{
for (int ui = 0; ui < tb.MuMesh.Length; ui++)
{
for (int wi = 0; wi < tb.FrequencyMesh.Length; wi++)
{
string filename_re = string.Format("{0}.re.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
string filename_im = string.Format("{0}.im.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
string filename_mag = string.Format("{0}.mag.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
Complex maxvalue = new Complex(double.MinValue, double.MinValue);
Complex minvalue = new Complex(double.MaxValue, double.MaxValue);
using (StreamWriter w_re = new StreamWriter(filename_re))
using (StreamWriter w_im = new StreamWriter(filename_im))
using (StreamWriter w_mag = new StreamWriter(filename_mag))
{
double last_t;
double last_s;
tb.QPlane.GetPlaneST(tb.QPlane.AllKpts[0], out last_s, out last_t);
for (int qi = 0; qi < tb.QPlane.AllKpts.Count; qi++)
{
Vector3 qpt = tb.QPlane.AllKpts[qi];
List<int> orbitalMap;
double s, t;
tb.QPlane.GetPlaneST(tb.QPlane.AllKpts[qi], out s, out t);
if (Math.Abs(t - last_t) > 1e-6)
{
w_re.WriteLine();
w_im.WriteLine();
w_mag.WriteLine();
}
int kindex =
tb.QPlane.IrreducibleIndex(qpt, tb.Lattice, tb.Symmetries, out orbitalMap);
int index = GetRpaIndex(rpa, kindex,
tb.TemperatureMesh[ti],
tb.FrequencyMesh[wi],
tb.MuMesh[ui]);
int newL1 = tb.Symmetries.TransformOrbital(orbitalMap, l1);
int newL2 = tb.Symmetries.TransformOrbital(orbitalMap, l2);
int newL3 = tb.Symmetries.TransformOrbital(orbitalMap, l3);
int newL4 = tb.Symmetries.TransformOrbital(orbitalMap, l4);
int newii = GetIndex(tb, newL1, newL2);
int newjj = GetIndex(tb, newL3, newL4);
Complex val = g(rpa[index])[newii, newjj];
w_re.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.RealPart);
w_im.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.ImagPart);
w_mag.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.Magnitude);
if (val.RealPart > maxvalue.RealPart) maxvalue.RealPart = val.RealPart;
if (val.ImagPart > maxvalue.ImagPart) maxvalue.ImagPart = val.ImagPart;
if (val.RealPart < minvalue.RealPart) minvalue.RealPart = val.RealPart;
if (val.ImagPart < minvalue.ImagPart) minvalue.ImagPart = val.ImagPart;
last_t = t;
last_s = s;
}
}
for (int i = 0; i < 3; i++)
{
string filename;
switch (i)
{
case 0: filename = filename_re; break;
case 1: filename = filename_im; break;
case 2: filename = filename_mag; break;
default:
continue;
}
string gpfilename = "gnuplot." + filename;
//minvalue.RealPart = Math.Floor(minvalue.RealPart);
//maxvalue.RealPart = Math.Ceiling(maxvalue.RealPart);
using (StreamWriter w = new StreamWriter(gpfilename))
{
w.WriteLine("#!/usr/bin/gnuplot");
//w.WriteLine("set pm3d at bs flush center ftriangles scansbackward interpolate 1,1");
w.WriteLine("set pm3d map flush center ftriangles scansbackward interpolate 5,5");
w.WriteLine("set palette rgbformula 23,9,-36");
//w.WriteLine("set border 895");
w.WriteLine("set key off");
//w.WriteLine("set zrange [{0}:{1}]", minvalue.RealPart, maxvalue.RealPart);
// label z = minvalue - 0.5 * (maxvalue - minvalue)
// set label 1 "G" at 0,0,1 font "Symbol" center front
w.WriteLine("splot '{0}' with pm3d", filename);
}
}
}
baseIndex += QMesh.Count;
}
}
}
}
}
}
}
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 CalcOnSiteInteraction(TightBinding tb, Matrix _S, Matrix _C, InteractionPair interaction)
{
foreach (int l1 in interaction.OrbitalsLeft)
{
foreach (int l2 in interaction.OrbitalsLeft)
{
foreach (int l3 in interaction.OrbitalsRight)
{
foreach (int l4 in interaction.OrbitalsRight)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
if (l1 == l2 && l2 == l3 && l3 == l4)
{
_S[i, j] += interaction.HubbardU;
_C[i, j] += interaction.HubbardU;
}
else if (l1 == l4 && l4 != l2 && l2 == l3)
{
_S[i, j] += interaction.InterorbitalU;
_C[i, j] += (-interaction.InterorbitalU + interaction.Exchange);
}
else if (l1 == l2 && l2 != l3 && l3 == l4)
{
_S[i, j] += interaction.Exchange;
_C[i, j] += 2 * interaction.InterorbitalU - interaction.Exchange;
}
else if (l1 == l3 && l3 != l2 && l2 == l4)
{
_S[i, j] += interaction.PairHopping;
_C[i, j] += interaction.PairHopping;
}
}
}
}
}
}
private void CalcOffSiteInteraction(TightBinding tb, Matrix _S, Matrix _C, InteractionPair interaction, double structureFactor)
{
foreach (int l1 in interaction.OrbitalsLeft)
{
foreach (int l2 in interaction.OrbitalsLeft)
{
foreach (int l3 in interaction.OrbitalsRight)
{
foreach (int l4 in interaction.OrbitalsRight)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
double Sval = 0, Cval = 0;
if (l1 == l2 && l2 == l3 && l3 == l4)
{
Sval = -0.5 * interaction.Exchange * structureFactor;
Cval = (2 * interaction.InterorbitalU - 0.5 * interaction.Exchange) * structureFactor;
}
else if (l1 == l2 && l2 != l3 && l3 == l4)
{
Sval = -0.25 * interaction.Exchange * structureFactor;
Cval = (2 * interaction.InterorbitalU - 0.5 * interaction.Exchange) * structureFactor;
}
_S[i, j] += Sval;
_S[j, i] += Sval;
_C[i, j] += Cval;
_C[j, i] += Cval;
}
}
}
}
}
private void VerifySymmetry(TightBinding tb, Matrix S, int a, int b)
{
for (int m1 = 0; m1 < 2; m1++)
{
for (int m2 = 0; m2 < 2; m2++)
{
for (int m3 = 0; m3 < 2; m3++)
{
for (int m4 = 0; m4 < 2; m4++)
{
int l1 = Select(m1, a, b);
int l2 = Select(m2, a, b);
int l3 = Select(m3, a, b);
int l4 = Select(m4, a, b);
int a1 = Select(m1, b, a);
int a2 = Select(m2, b, a);
int a3 = Select(m3, b, a);
int a4 = Select(m4, b, a);
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
int ii = GetIndex(tb, a1, a2);
int jj = GetIndex(tb, a3, a4);
var diff = S[i, j] - S[ii, jj];
if (diff.Magnitude > 1e-8)
{
Output.WriteLine("ERROR: Failed to verify symmetry.");
Output.WriteLine(" a = {0} b = {1}", a, b);
Output.WriteLine(" L = {0}{1}{2}{3}", l1, l2, l3, l4);
Output.WriteLine(" A = {0}{1}{2}{3}", a1, a2, a3, a4);
Output.WriteLine(" ij = {0},{1} {2},{3}", i, j, ii, jj);
Output.WriteLine(" M[i,j] = {0} {1}", S[i,j], S[ii,jj]);
Output.WriteLine(" diff = {0}", diff.Magnitude);
try
{
throw new Exception("blah");
}
catch(Exception e)
{
Output.WriteLine(e.StackTrace);
}
Environment.Exit(4);
}
}
}
}
}
}
void SetTemperature(TightBinding tb, double temperature, double mu)
{
//currentTemperature = value;
Beta = 1 / temperature;
tb.KMesh.SetTemperature(temperature, mu);
}
Matrix CalcX0(TightBinding tb, double freq, Vector3 q)
{
int orbitalCount = tb.Orbitals.Count;
int size = orbitalCount * orbitalCount;
Matrix x = new Matrix(size, size);
Complex denom_factor = new Complex(0, 1e-4);
//StreamWriter w = new StreamWriter(string.Format("qcont.{0}", q.ToString("0.000")));
//bool writeThis = false;
for (int l1 = 0; l1 < orbitalCount; l1++)
{
for (int l4 = 0; l4 < orbitalCount; l4++)
{
for (int l3 = l1; l3 < orbitalCount; l3++)
{
for (int l2 = l4; l2 < orbitalCount; l2++)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
bool foundSymmetry = false;
//if (l1 == 0 && l2 == 0 && l3 == 0 && l4 == 0)
// writeThis = true;
//else
//writeThis = false;
//if (writeThis)
// w.WriteLine("{0}{1}{2}{3}", l1, l2, l3, l4);
for (int s = 0; s < tb.Symmetries.Count; s++)
{
Symmetry sym = tb.Symmetries[s];
if (sym.OrbitalTransform == null || sym.OrbitalTransform.Count == 0)
{
continue;
}
int newL1 = sym.OrbitalTransform[l1];
int newL2 = sym.OrbitalTransform[l2];
int newL3 = sym.OrbitalTransform[l3];
int newL4 = sym.OrbitalTransform[l4];
int newI = GetIndex(tb, newL1, newL2);
int newJ = GetIndex(tb, newL3, newL4);
if (newI == i && newJ == j)
{
continue;
}
foundSymmetry = true;
if (newL1 > l1)
{
foundSymmetry = false;
}
if (newL2 > l2)
{
foundSymmetry = false;
}
if (newL3 > l3)
{
foundSymmetry = false;
}
if (newL4 > l4)
{
foundSymmetry = false;
}
if (foundSymmetry)
{
x[i, j] = x[newI, newJ];
x[j, i] = x[i, j].Conjugate();
break;
}
}
if (foundSymmetry)
{
continue;
}
Complex total = 0;
for (int allkindex = 0; allkindex < tb.KMesh.AllKpts.Count; allkindex++)
{
Complex val = 0;
Vector3 k = tb.KMesh.AllKpts[allkindex];
Vector3 kq = k + q;
//List<int> kOrbitalMap;
//List<int> kqOrbitalMap;
//int kindex = tb.KMesh.IrreducibleIndex(k, tb.Lattice, tb.Symmetries, out kOrbitalMap);
//int kqindex = tb.KMesh.IrreducibleIndex(kq, tb.Lattice, tb.Symmetries, out kqOrbitalMap);
int kindex = tb.KMesh.AllKindex(k, tb.Lattice);
int kqindex = tb.KMesh.AllKindex(kq, tb.Lattice);
System.Diagnostics.Debug.Assert(kindex == allkindex);
//int newL1 = TransformOrbital(kqOrbitalMap, l1);
//int newL2 = TransformOrbital(kOrbitalMap, l2);
//int newL3 = TransformOrbital(kqOrbitalMap, l3);
//int newL4 = TransformOrbital(kOrbitalMap, l4);
for (int n1 = 0; n1 < orbitalCount; n1++)
{
Wavefunction wfk = Bands(tb, kindex, n1);
double e1 = wfk.Energy;
double f1 = wfk.FermiFunction;
for (int n2 = 0; n2 < orbitalCount; n2++)
{
Wavefunction wfq = Bands(tb, kqindex, n2);
double e2 = wfq.Energy;
double f2 = wfq.FermiFunction;
Complex coeff =
wfq.Coeffs[l1] * wfq.Coeffs[l4].Conjugate() *
wfk.Coeffs[l3] * wfk.Coeffs[l2].Conjugate();
if (coeff == 0)
{
continue;
}
if (f1 < 1e-15 && f2 < 1e-15)
{
continue;
}
Complex denom_p = (e2 - e1 + freq + denom_factor);
//Complex denom_n = (e2 - e1 - freq - denom_factor);
//Complex lindhard = (f1 - f2) * (1.0 / denom_p + 1.0 / denom_n);
Complex lindhard = (f1 - f2) * (1.0 / denom_p);
Complex contrib = coeff * lindhard;
if (Math.Abs(f1 - f2) < 1e-11 && freq == 0.0)
{
contrib = coeff * f1 * (1 - f1) * Beta;
}
//w.Write("{0} {1} {2} {3} ", kindex, kqindex, n1, n2);
//w.WriteLine("{0} {1} {2} {3} {4}", coeff, e1, e2, f1, f2);
if (double.IsNaN(contrib.RealPart) || double.IsNaN(contrib.ImagPart))
{
throw new Exception("Found NaN when evaluating X0");
}
val += contrib;
}
}
//w.WriteLine("{0} {1} total {2} + {3}i", kindex, kqindex,
// Math.Round(val.RealPart, 4), Math.Round(val.ImagPart, 4));
//Output.WriteLine(tb.KMesh.AllKpts[kindex].Weight.ToString());
val *= tb.KMesh.AllKpts[kindex].Weight;
total += val;
//if (writeThis)
// w.WriteLine("{0} {1} {2}", allkindex, total, val);
}
x[i, j] = total;
x[j, i] = total.Conjugate();
//if (writeThis)
//{
// w.WriteLine("total for {0}{1}{2}{3}: {4}", l1, l2, l3, l4, total);
// w.WriteLine("---------------------");
//}
}
}
}
}
//w.Close();
return(x);
}
public TbInputFileReader(string filename, TightBinding tb)
: base(filename)
{
this.tb = tb;
}
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);
}
int GetIndex(TightBinding tb, int l1, int l2)
{
// if this changes, be sure to correct the way
// x[i,j] and x[j,i] are set in CalcX0.
return(l1 * tb.Orbitals.Count + l2);
}
double InteractionAdjustment(List<RpaParams> rpa, Matrix[] S, Matrix[] C, TightBinding tb)
{
double largest = double.MinValue;
RpaParams largestParams = null;
bool Cdiv = false;
for (int i = 0; i < rpa.Count; i++)
{
RpaParams p = rpa[i];
Matrix x0 = p.X0;
double lv = LargestPositiveEigenvalue(x0 * S[i]);
if (lv > largest)
{
largest = lv;
largestParams = p;
Cdiv = false;
}
lv = LargestPositiveEigenvalue(-x0 * C[i]);
if (lv > largest)
{
largest = lv;
largestParams = p;
Cdiv = true;
}
}
if (largest >= 1)
{
Output.WriteLine("Interaction should be reduced to avoid divergence.", largest);
}
Output.WriteLine("Largest eigenvalue of denominator found at:");
Output.WriteLine(" Eigenvalue: {0}", largest);
Output.WriteLine(" {0} susceptibility", Cdiv ? "Charge" : "Spin");
Output.WriteLine(" q = {0}", largestParams.QptValue);
Output.WriteLine(" Temperature = {0}", largestParams.Temperature);
Output.WriteLine(" Chemical Potential = {0}", largestParams.ChemicalPotential);
Output.WriteLine(" Frequency = {0}", largestParams.Frequency);
largest /= tb.Interactions.MaxEigenvalue;
Output.WriteLine();
return 1 / largest;
}
private void CalcSpinChargeMatrices(TightBinding tb, List<RpaParams> rpa, out Matrix[] S, out Matrix[] C)
{
S = new Matrix[rpa.Count];
C = new Matrix[rpa.Count];
for (int rpa_index = 0; rpa_index < rpa.Count; rpa_index++)
{
Vector3 q = rpa[rpa_index].QptValue;
int size = tb.Orbitals.Count * tb.Orbitals.Count;
Matrix _S = new Matrix(size, size);
Matrix _C = new Matrix(size, size);
foreach (var interaction in tb.Interactions)
{
double structureFactor = interaction.StructureFactor(q);
if (interaction.OnSite)
CalcOnSiteInteraction(tb, _S, _C, interaction);
else
CalcOffSiteInteraction(tb, _S, _C, interaction, structureFactor);
}
System.Diagnostics.Debug.Assert(_S.IsSymmetric);
System.Diagnostics.Debug.Assert(_C.IsSymmetric);
S[rpa_index] = _S;
C[rpa_index] = _C;
}
}
void Run(string inputfile)
{
TightBinding tb = new TightBinding();
tb.LoadTB(inputfile);
tb.RunTB();
bool ranRPA = false;
SetCpus();
if (tb.UseQPlane && tb.QPlane != null && tb.QPlane.Kpts.Count > 0)
{
RunRpa(tb, tb.QPlane, true);
ranRPA = true;
}
if (tb.QMesh != null)
{
RunRpa(tb, tb.QMesh, false);
ranRPA = true;
}
if (!ranRPA)
Output.WriteLine("No q-points defined, so we will not run the RPA.");
}
public Wavefunction Bands(TightBinding tb, int kpt, int band)
{
return tb.KMesh.AllKpts[kpt].Wavefunctions[band];
}
private void SaveByTemperature(TightBinding tb, List<KPoint> QMesh, List<RpaParams> rpa, MatrixGetter g, string name)
{
rpa.Sort(RpaParams.TemperatureComparison);
Complex[] chisum = new Complex[rpa.Count];
double[] chimag = new double[rpa.Count];
double[] chimagsqr = new double[rpa.Count];
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 i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
// organize by temperature
string filename = string.Format(
"temperature/{0}.{1}{2}{3}{4}.T", name, l1, l2, l3, l4);
double lastFreq = double.MinValue;
double lastMu = double.MinValue;
double lastq = int.MinValue;
using (StreamWriter w = new StreamWriter(filename))
{
for (int index = 0; index < rpa.Count; index++)
{
bool newline = false;
newline |= ChangeValue(ref lastFreq, rpa[index].Frequency);
newline |= ChangeValue(ref lastMu, rpa[index].ChemicalPotential);
newline |= ChangeValue(ref lastq, rpa[index].Qindex);
if (newline)
{
w.WriteLine();
w.WriteLine("# Frequency: {0}", rpa[index].Frequency);
w.WriteLine("# Chemical Potential: {0}", rpa[index].ChemicalPotential);
w.WriteLine("# Q: {0}", QMesh[rpa[index].Qindex]);
w.WriteLine("#");
w.WriteLine("# Temperature\tRe(Chi)\tIm(Chi)");
}
Complex val = g(rpa[index])[i, j];
chisum[index] += val;
chimag[index] += val.Magnitude;
chimagsqr[index] += val.MagnitudeSquared;
w.WriteLine("\t{0:0.000000}\t{1:0.0000000}\t{2:0.0000000}",
rpa[index].Temperature, val.RealPart, val.ImagPart);
}
}
}
}
}
}
}
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);
}
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 Wavefunction Bands(TightBinding tb, int kpt, int band)
{
return(tb.KMesh.AllKpts[kpt].Wavefunctions[band]);
}
Matrix CalcX0(TightBinding tb, double freq, Vector3 q)
{
int orbitalCount = tb.Orbitals.Count;
int size = orbitalCount * orbitalCount;
Matrix x = new Matrix(size, size);
Complex denom_factor = new Complex(0, 1e-4);
//StreamWriter w = new StreamWriter(string.Format("qcont.{0}", q.ToString("0.000")));
//bool writeThis = false;
for (int l1 = 0; l1 < orbitalCount; l1++)
{
for (int l4 = 0; l4 < orbitalCount; l4++)
{
for (int l3 = l1; l3 < orbitalCount; l3++)
{
for (int l2 = l4; l2 < orbitalCount; l2++)
{
int i = GetIndex(tb, l1, l2);
int j = GetIndex(tb, l3, l4);
bool foundSymmetry = false;
//if (l1 == 0 && l2 == 0 && l3 == 0 && l4 == 0)
// writeThis = true;
//else
//writeThis = false;
//if (writeThis)
// w.WriteLine("{0}{1}{2}{3}", l1, l2, l3, l4);
for (int s = 0; s < tb.Symmetries.Count; s++)
{
Symmetry sym = tb.Symmetries[s];
if (sym.OrbitalTransform == null || sym.OrbitalTransform.Count == 0)
continue;
int newL1 = sym.OrbitalTransform[l1];
int newL2 = sym.OrbitalTransform[l2];
int newL3 = sym.OrbitalTransform[l3];
int newL4 = sym.OrbitalTransform[l4];
int newI = GetIndex(tb, newL1, newL2);
int newJ = GetIndex(tb, newL3, newL4);
if (newI == i && newJ == j)
continue;
foundSymmetry = true;
if (newL1 > l1) foundSymmetry = false;
if (newL2 > l2) foundSymmetry = false;
if (newL3 > l3) foundSymmetry = false;
if (newL4 > l4) foundSymmetry = false;
if (foundSymmetry)
{
x[i, j] = x[newI, newJ];
x[j, i] = x[i, j].Conjugate();
break;
}
}
if (foundSymmetry)
continue;
Complex total = 0;
for (int allkindex = 0; allkindex < tb.KMesh.AllKpts.Count; allkindex++)
{
Complex val = 0;
Vector3 k = tb.KMesh.AllKpts[allkindex];
Vector3 kq = k + q;
//List<int> kOrbitalMap;
//List<int> kqOrbitalMap;
//int kindex = tb.KMesh.IrreducibleIndex(k, tb.Lattice, tb.Symmetries, out kOrbitalMap);
//int kqindex = tb.KMesh.IrreducibleIndex(kq, tb.Lattice, tb.Symmetries, out kqOrbitalMap);
int kindex = tb.KMesh.AllKindex(k, tb.Lattice);
int kqindex = tb.KMesh.AllKindex(kq, tb.Lattice);
System.Diagnostics.Debug.Assert(kindex == allkindex);
//int newL1 = TransformOrbital(kqOrbitalMap, l1);
//int newL2 = TransformOrbital(kOrbitalMap, l2);
//int newL3 = TransformOrbital(kqOrbitalMap, l3);
//int newL4 = TransformOrbital(kOrbitalMap, l4);
for (int n1 = 0; n1 < orbitalCount; n1++)
{
Wavefunction wfk = Bands(tb, kindex, n1);
double e1 = wfk.Energy;
double f1 = wfk.FermiFunction;
for (int n2 = 0; n2 < orbitalCount; n2++)
{
Wavefunction wfq = Bands(tb, kqindex, n2);
double e2 = wfq.Energy;
double f2 = wfq.FermiFunction;
Complex coeff =
wfq.Coeffs[l1] * wfq.Coeffs[l4].Conjugate() *
wfk.Coeffs[l3] * wfk.Coeffs[l2].Conjugate();
if (coeff == 0) continue;
if (f1 < 1e-15 && f2 < 1e-15) continue;
Complex denom_p = (e2 - e1 + freq + denom_factor);
//Complex denom_n = (e2 - e1 - freq - denom_factor);
//Complex lindhard = (f1 - f2) * (1.0 / denom_p + 1.0 / denom_n);
Complex lindhard = (f1 - f2) * (1.0 / denom_p);
Complex contrib = coeff * lindhard;
if (Math.Abs(f1 - f2) < 1e-11 && freq == 0.0)
{
contrib = coeff * f1 * (1 - f1) * Beta;
}
//w.Write("{0} {1} {2} {3} ", kindex, kqindex, n1, n2);
//w.WriteLine("{0} {1} {2} {3} {4}", coeff, e1, e2, f1, f2);
if (double.IsNaN(contrib.RealPart) || double.IsNaN(contrib.ImagPart))
{
throw new Exception("Found NaN when evaluating X0");
}
val += contrib;
}
}
//w.WriteLine("{0} {1} total {2} + {3}i", kindex, kqindex,
// Math.Round(val.RealPart, 4), Math.Round(val.ImagPart, 4));
//Output.WriteLine(tb.KMesh.AllKpts[kindex].Weight.ToString());
val *= tb.KMesh.AllKpts[kindex].Weight;
total += val;
//if (writeThis)
// w.WriteLine("{0} {1} {2}", allkindex, total, val);
}
x[i, j] = total;
x[j, i] = total.Conjugate();
//if (writeThis)
//{
// w.WriteLine("total for {0}{1}{2}{3}: {4}", l1, l2, l3, l4, total);
// w.WriteLine("---------------------");
//}
}
}
}
}
//w.Close();
return x;
}
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;
}
/// <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();
}
}
}
int GetIndex(TightBinding tb, int l1, int l2)
{
// if this changes, be sure to correct the way
// x[i,j] and x[j,i] are set in CalcX0.
return l1 * tb.Orbitals.Count + l2;
}
public TbInputFileReader(string filename, TightBinding tb)
: base(filename)
{
this.tb = tb;
}
private void SaveByQPlane(TightBinding tb, List <KPoint> QMesh, List <RpaParams> rpa, MatrixGetter g, string name)
{
rpa.Sort(RpaParams.QIndexComparison);
Complex[] chisum = new Complex[rpa.Count];
double[] chimag = new double[rpa.Count];
double[] chimagsqr = new double[rpa.Count];
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++)
{
double lastFreq = double.MinValue;
double lastMu = double.MinValue;
double lastq = int.MinValue;
int baseIndex = 0;
for (int ti = 0; ti < tb.TemperatureMesh.Length; ti++)
{
for (int ui = 0; ui < tb.MuMesh.Length; ui++)
{
for (int wi = 0; wi < tb.FrequencyMesh.Length; wi++)
{
string filename_re = string.Format("{0}.re.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
string filename_im = string.Format("{0}.im.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
string filename_mag = string.Format("{0}.mag.{1}{2}{3}{4}.w{5}.T{6}.u{7}.qm",
name, l1, l2, l3, l4, wi, ti, ui);
Complex maxvalue = new Complex(double.MinValue, double.MinValue);
Complex minvalue = new Complex(double.MaxValue, double.MaxValue);
using (StreamWriter w_re = new StreamWriter(filename_re))
using (StreamWriter w_im = new StreamWriter(filename_im))
using (StreamWriter w_mag = new StreamWriter(filename_mag))
{
double last_t;
double last_s;
tb.QPlane.GetPlaneST(tb.QPlane.AllKpts[0], out last_s, out last_t);
for (int qi = 0; qi < tb.QPlane.AllKpts.Count; qi++)
{
Vector3 qpt = tb.QPlane.AllKpts[qi];
List <int> orbitalMap;
double s, t;
tb.QPlane.GetPlaneST(tb.QPlane.AllKpts[qi], out s, out t);
if (Math.Abs(t - last_t) > 1e-6)
{
w_re.WriteLine();
w_im.WriteLine();
w_mag.WriteLine();
}
int kindex =
tb.QPlane.IrreducibleIndex(qpt, tb.Lattice, tb.Symmetries, out orbitalMap);
int index = GetRpaIndex(rpa, kindex,
tb.TemperatureMesh[ti],
tb.FrequencyMesh[wi],
tb.MuMesh[ui]);
int newL1 = tb.Symmetries.TransformOrbital(orbitalMap, l1);
int newL2 = tb.Symmetries.TransformOrbital(orbitalMap, l2);
int newL3 = tb.Symmetries.TransformOrbital(orbitalMap, l3);
int newL4 = tb.Symmetries.TransformOrbital(orbitalMap, l4);
int newii = GetIndex(tb, newL1, newL2);
int newjj = GetIndex(tb, newL3, newL4);
Complex val = g(rpa[index])[newii, newjj];
w_re.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.RealPart);
w_im.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.ImagPart);
w_mag.WriteLine(" {0} {1} {2:0.0000000}", s, t, val.Magnitude);
if (val.RealPart > maxvalue.RealPart)
{
maxvalue.RealPart = val.RealPart;
}
if (val.ImagPart > maxvalue.ImagPart)
{
maxvalue.ImagPart = val.ImagPart;
}
if (val.RealPart < minvalue.RealPart)
{
minvalue.RealPart = val.RealPart;
}
if (val.ImagPart < minvalue.ImagPart)
{
minvalue.ImagPart = val.ImagPart;
}
last_t = t;
last_s = s;
}
}
for (int i = 0; i < 3; i++)
{
string filename;
switch (i)
{
case 0: filename = filename_re; break;
case 1: filename = filename_im; break;
case 2: filename = filename_mag; break;
default:
continue;
}
string gpfilename = "gnuplot." + filename;
//minvalue.RealPart = Math.Floor(minvalue.RealPart);
//maxvalue.RealPart = Math.Ceiling(maxvalue.RealPart);
using (StreamWriter w = new StreamWriter(gpfilename))
{
w.WriteLine("#!/usr/bin/gnuplot");
//w.WriteLine("set pm3d at bs flush center ftriangles scansbackward interpolate 1,1");
w.WriteLine("set pm3d map flush center ftriangles scansbackward interpolate 5,5");
w.WriteLine("set palette rgbformula 23,9,-36");
//w.WriteLine("set border 895");
w.WriteLine("set key off");
//w.WriteLine("set zrange [{0}:{1}]", minvalue.RealPart, maxvalue.RealPart);
// label z = minvalue - 0.5 * (maxvalue - minvalue)
// set label 1 "G" at 0,0,1 font "Symbol" center front
w.WriteLine("splot '{0}' with pm3d", filename);
}
}
}
baseIndex += QMesh.Count;
}
}
}
}
}
}
}
