public HoppingPair Find(int left, int right)
{
HoppingPair retval = this.Find(x => x.Left == left && x.Right == right);
if (retval == null)
{
HoppingPair p = this.Find(x => x.Right == left && x.Left == right);
if (p == null)
{
return(null);
}
// generate symmetric hopping if it doesn't exist.
retval = new HoppingPair(left, right);
for (int i = 0; i < p.Hoppings.Count; i++)
{
HoppingValue v = new HoppingValue();
v.Value = p.Hoppings[i].Value;
v.R = -p.Hoppings[i].R;
retval.Hoppings.Add(v);
}
this.Add(retval);
}
return(retval);
}
void ReadHoppingsSection()
{
if (tb.hoppings != null)
{
ThrowEx("Multiple hoppings sections found.");
}
if (LineType != LineType.NewSubSection)
{
ThrowEx("Hoppings section must start with :..: delimited section.");
}
tb.hoppings = new HoppingPairList();
while (!EOF && LineType != LineType.NewSection)
{
string[] values = ReadSubSectionParameters();
int left = int.Parse(values[0]) - 1;
int right = int.Parse(values[1]) - 1;
HoppingPair p = new HoppingPair(left, right);
tb.hoppings.Add(p);
//Output.WriteLine("Reading hoppings for {0}-{1}", left + 1, right + 1);
ReadNextLine();
while (LineType == LineType.Hopping || LineType == LineType.Numeric)
{
List <string> vals = new List <string>();
vals.AddRange(Line.Replace('\t', ' ').Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries));
if (vals[0] == "T=")
{
vals.RemoveAt(0);
}
if (vals[3] == "hop=")
{
vals.RemoveAt(3);
}
double value = double.Parse(vals[vals.Count - 1]);
Vector3 loc = new Vector3(double.Parse(vals[0]), double.Parse(vals[1]), double.Parse(vals[2]));
HoppingValue v = new HoppingValue();
v.Value = value;
v.R = loc;
p.Hoppings.Add(v);
ReadNextLine();
}
//Output.WriteLine("Count: {0}", p.Hoppings.Count);
}
}
public bool Contains(HoppingValue val)
{
foreach (HoppingValue a in Hoppings)
{
if (a.Value != val.Value)
{
continue;
}
if ((a.R - val.R).Magnitude > 1e-6)
{
continue;
}
//Console.WriteLine("hop: {0} {1} {2} {3}",
// a.Value, a.BravaisVector,
// val.Value, val.BravaisVector);
return(true);
}
return(false);
}
public Matrix CalcHamiltonian(Vector3 kpt)
{
Matrix m = new Matrix(Orbitals.Count, Orbitals.Count);
kpt *= 2 * Math.PI;
for (int i = 0; i < Orbitals.Count; i++)
{
for (int j = 0; j < Orbitals.Count; j++)
{
HoppingPair p = Hoppings.FindOrThrow(i, j);
Complex val = new Complex();
for (int k = 0; k < p.Hoppings.Count; k++)
{
HoppingValue hop = p.Hoppings[k];
Vector3 R = hop.R;
Complex newval = hop.Value *
Complex.Exp(new Complex(0, kpt.DotProduct(R)));
val += newval;
}
m[i, j] = val;
}
}
if (m.IsHermitian == false)
{
throw new Exception("Hamiltonian at k = " + kpt.ToString() + " is not Hermitian.");
}
return(m);
}
void ApplySymmetries()
{
List <Matrix> validSyms = new List <Matrix>();
Matrix reduce = new Matrix(3, 3);
reduce.SetRows(tb.lattice.G1, tb.lattice.G2, tb.lattice.G3);
int symIndex = 0;
using (StreamWriter s = new StreamWriter("syms"))
{
foreach (var sym in GetPossibleSymmetries())
{
symIndex++;
s.WriteLine();
s.WriteLine("Applying symmetry " + symIndex.ToString() + ":");
s.WriteLine(sym);
Matrix lat = new Matrix(3, 3);
lat.SetColumns(sym * tb.lattice.A1, sym * tb.lattice.A2, sym * tb.lattice.A3);
lat = reduce * lat;
s.WriteLine("Lattice vector test...");
if (CheckLatticeSymmetry(lat) == false)
{
goto fail;
}
Dictionary <int, int> sitemap = new Dictionary <int, int>();
s.WriteLine("Generating site map...");
for (int i = 0; i < tb.sites.Count; i++)
{
var site = tb.sites[i];
Vector3 loc = sym * site.Location;
int index = tb.Orbitals.FindIndex(tb.lattice, loc);
if (index == -1)
{
s.WriteLine("Failed to map site " + i.ToString());
goto fail;
}
sitemap[i] = index;
s.WriteLine(" " + i.ToString() + " => " + index.ToString());
}
HoppingPairList newHops = new HoppingPairList();
// rotate hoppings
for (int i = 0; i < tb.hoppings.Count; i++)
{
var pair = tb.hoppings[i];
int newleft = sitemap[pair.Left];
int newright = sitemap[pair.Right];
HoppingPair newPair = new HoppingPair(newleft, newright);
newHops.Add(newPair);
foreach (var hop in pair.Hoppings)
{
HoppingValue v = new HoppingValue();
v.Value = hop.Value;
v.R = sym * hop.R;
newPair.Hoppings.Add(v);
}
}
s.WriteLine("Performing hopping test...");
if (newHops.Equals(tb.hoppings) == false)
{
goto fail;
}
s.WriteLine("Success.");
validSyms.Add(sym);
continue;
fail:
s.WriteLine("Failed.");
}
// now apply symmetries to reduce k-points in kmesh
int initialKptCount = tb.kmesh.Kpts.Count;
System.Diagnostics.Stopwatch watch = new System.Diagnostics.Stopwatch();
watch.Start();
foreach (var sym in validSyms)
{
for (int i = 0; i < tb.kmesh.Kpts.Count; i++)
{
KPoint kpt = tb.kmesh.Kpts[i];
Vector3 trans = kpt.Value;
/*
* for (int j = 0; j < 3; j++)
* {
* trans = sym * trans;
*
* int index = kmesh.IndexOf(trans, i+1);
*
* if (index == -1)
* continue;
*
* kmesh.Kpts.RemoveAt(index);
* kpt.Weight ++;
*
* }
*/
}
}
watch.Stop();
string fmt = string.Format("{0} total kpts, {1} irreducible kpts. Applying symmetries took {2} seconds.",
initialKptCount, tb.kmesh.Kpts.Count, watch.ElapsedMilliseconds / 1000);
Output.WriteLine(fmt);
s.WriteLine(fmt);
}
}
public bool Equals(HoppingValue v)
{
return(Math.Abs(Value - v.Value) < 1e-6 &&
(R - v.R).Magnitude < 1e-6);
}