private int GetGreenIndex(RpaParams[] plist)
{
if (plist.Length == 1)
return 0;
Console.WriteLine();
Console.WriteLine("Found {0} Green's functions.", plist.Length);
for(;;)
{
Console.Write("Enter index to use (1-{0}): ", plist.Length);
int index;
if (int.TryParse(Console.ReadLine(), out index) == false)
continue;
Console.WriteLine();
Console.WriteLine("Chose Green's function index {0}.", index);
Console.WriteLine(" Temperature: {0}", plist[index].Temperature);
Console.WriteLine(" Frequency: {0}", plist[index].Frequency);
Console.WriteLine(" Mu: {0}", plist[index].ChemicalPotential);
Console.WriteLine();
Console.Write("Is this ok (y/n)? ");
var key = Console.ReadKey();
if (key.Key == ConsoleKey.Y)
{
return index;
}
}
}
/// <summary>
/// Sorts by temperature, chemical potential, frequency, qindex.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public static int QIndexComparison(RpaParams x, RpaParams y)
{
if (x.Temperature != y.Temperature)
return x.Temperature.CompareTo(y.Temperature);
if (x.ChemicalPotential != y.ChemicalPotential)
return x.ChemicalPotential.CompareTo(y.ChemicalPotential);
if (x.Frequency != y.Frequency)
return x.Frequency.CompareTo(y.Frequency);
return x.Qindex.CompareTo(y.Qindex);
}
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 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 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;
}
/// <summary>
/// Sorts by temperature, chemical potential, frequency, qindex.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public static int QIndexComparison(RpaParams x, RpaParams y)
{
if (x.Temperature != y.Temperature)
{
return(x.Temperature.CompareTo(y.Temperature));
}
if (x.ChemicalPotential != y.ChemicalPotential)
{
return(x.ChemicalPotential.CompareTo(y.ChemicalPotential));
}
if (x.Frequency != y.Frequency)
{
return(x.Frequency.CompareTo(y.Frequency));
}
return(x.Qindex.CompareTo(y.Qindex));
}
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);
};
}
}
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 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);
};
}
}