private static Symmetry ParseSymmetry(string text)
{
Match rotText = rotation.Match(text);
MatchCollection values = rotationValues.Matches(rotText.ToString());
Matrix matrix = new Matrix(3, 3);
for (int i = 0; i < 3; i++)
{
Vector3 opVec = GetOperationVector(values[i].ToString());
matrix.SetRow(i, opVec);
}
Match transText = translation.Match(text);
MatchCollection transValues = translationValues.Matches(transText.ToString());
Vector3 trans = new Vector3();
for (int i = 0; i < 3; i++)
{
trans[i] = EvaluateFraction(transValues[i].ToString());
}
Symmetry sym = new Symmetry(matrix, trans);
return(sym);
}
public Symmetry Clone()
{
Symmetry x = new Symmetry(Value.Clone());
x.OrbitalTransform.AddRange(OrbitalTransform);
return x;
}
public Symmetry Clone()
{
Symmetry x = new Symmetry(Value.Clone());
x.OrbitalTransform.AddRange(OrbitalTransform);
return(x);
}
private bool DuplicateSymmetry(Symmetry newSym)
{
foreach (Symmetry sym in Symmetries)
{
if ((sym.Value - newSym.Value).IsZero)
{
return(true);
}
}
return(false);
}
private void GenerateSymmetries(Symmetry sym)
{
foreach (var s in PrimitiveSymmetries)
{
Symmetry newSym = Symmetry.Compose(sym, s);
if (DuplicateSymmetry(newSym))
{
continue;
}
Symmetries.Add(newSym);
GenerateSymmetries(newSym);
}
}
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 void GenerateSymmetries(Symmetry sym)
{
foreach (var s in PrimitiveSymmetries)
{
Symmetry newSym = Symmetry.Compose(sym, s);
if (DuplicateSymmetry(newSym))
continue;
Symmetries.Add(newSym);
GenerateSymmetries(newSym);
}
}
private bool DuplicateSymmetry(Symmetry newSym)
{
foreach (Symmetry sym in Symmetries)
{
if ((sym.Value - newSym.Value).IsZero)
return true;
}
return false;
}
private static Symmetry ParseSymmetry(string text)
{
Match rotText = rotation.Match(text);
MatchCollection values = rotationValues.Matches(rotText.ToString());
Matrix matrix = new Matrix(3, 3);
for (int i = 0; i < 3; i++)
{
Vector3 opVec = GetOperationVector(values[i].ToString());
matrix.SetRow(i, opVec);
}
Match transText = translation.Match(text);
MatchCollection transValues = translationValues.Matches(transText.ToString());
Vector3 trans = new Vector3();
for (int i = 0; i < 3; i++)
{
trans[i] = EvaluateFraction(transValues[i].ToString());
}
Symmetry sym = new Symmetry(matrix, trans);
return sym;
}
