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Grid/Grid/qcd/utils/Sp2n.impl
2023-06-23 15:34:08 +01:00

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// This file is #included into the body of the class template definition of
// GaugeGroup. So, image there to be
//
// template <int ncolour, class group_name>
// class GaugeGroup {
//
// around it.
//
// Please note that the unconventional file extension makes sure that it
// doesn't get found by the scripts/filelist during bootstrapping.
private:
template <ONLY_IF_Sp>
static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }
// Sp(2N) has N(2N+1) = 2N^2+N generators
//
// normalise the generators such that
// Trace ( Ta Tb) = 1/2 delta_ab
//
// N generators in the cartan, 2N^2 off
// off diagonal:
// there are 6 types named a,b,c,d and w,z
// abcd are N(N-1)/2 each while wz are N each
template <class cplx, ONLY_IF_Sp>
static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::Sp) {
// map lie index into type of generators: diagonal, abcd type, wz type
const int nsp = ncolour/2;
int diagIndex;
int aIndex, bIndex, cIndex, dIndex;
int wIndex, zIndex; // a,b,c,d are N(N-1)/2 and w,z are N
const int mod = nsp * (nsp - 1) * 0.5;
const int offdiag =
2 * nsp * nsp; // number of generators not in the cartan subalgebra
const int wmod = 4 * mod;
const int zmod = wmod + nsp;
if (lieIndex >= offdiag) {
diagIndex = lieIndex - offdiag; // 0, ... ,N-1
// std::cout << GridLogMessage << "diag type " << std::endl;
generatorDiagtype(diagIndex, ta);
return;
}
if ((lieIndex >= wmod) && (lieIndex < zmod)) {
// std::cout << GridLogMessage << "w type " << std::endl;
wIndex = lieIndex - wmod; // 0, ... ,N-1
generatorWtype(wIndex, ta);
return;
}
if ((lieIndex >= zmod) && (lieIndex < offdiag)) {
// std::cout << GridLogMessage << "z type " << std::endl;
// std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
// std::cout << GridLogMessage << "z mod " << zmod << std::endl;
zIndex = lieIndex - zmod; // 0, ... ,N-1
generatorZtype(zIndex, ta);
return;
}
if (lieIndex < mod) { // atype 0, ... , N(N-1)/2=mod
// std::cout << GridLogMessage << "a type " << std::endl;
aIndex = lieIndex;
// std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
generatorAtype(aIndex, ta);
return;
}
if ((lieIndex >= mod) && lieIndex < 2 * mod) { // btype mod, ... , 2mod-1
// std::cout << GridLogMessage << "b type " << std::endl;
bIndex = lieIndex - mod;
generatorBtype(bIndex, ta);
return;
}
if ((lieIndex >= 2 * mod) &&
lieIndex < 3 * mod) { // ctype 2mod, ... , 3mod-1
// std::cout << GridLogMessage << "c type " << std::endl;
cIndex = lieIndex - 2 * mod;
generatorCtype(cIndex, ta);
return;
}
if ((lieIndex >= 3 * mod) &&
lieIndex < wmod) { // ctype 3mod, ... , 4mod-1 = wmod-1
// std::cout << GridLogMessage << "d type " << std::endl;
dIndex = lieIndex - 3 * mod;
generatorDtype(dIndex, ta);
return;
}
} // end of generator
template <class cplx, ONLY_IF_Sp>
static void generatorDiagtype(int diagIndex, iGroupMatrix<cplx> &ta) {
// ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
const int nsp=ncolour/2;
ta = Zero();
RealD nrm = 1.0 / 2;
ta()()(diagIndex, diagIndex) = nrm;
ta()()(diagIndex + nsp, diagIndex + nsp) = -nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorAtype(int aIndex, iGroupMatrix<cplx> &ta) {
// ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
// with i<j and i=0,...,N-2
// follows that j=i+1, ... , N
int i1, i2;
const int nsp=ncolour/2;
ta = Zero();
RealD nrm = 1 / (2 * std::sqrt(2));
su2SubGroupIndex(i1, i2, aIndex);
ta()()(i1, i2) = 1;
ta()()(i2, i1) = 1;
ta()()(i1 + nsp, i2 + nsp) = -1;
ta()()(i2 + nsp, i1 + nsp) = -1;
ta = ta * nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorBtype(int bIndex, iGroupMatrix<cplx> &ta) {
// ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
// with i<j and i=0,...,N-2
// follows that j=i+1, ... , N-1
const int nsp=ncolour/2;
int i1, i2;
ta = Zero();
cplx i(0.0, 1.0);
RealD nrm = 1 / (2 * std::sqrt(2));
su2SubGroupIndex(i1, i2, bIndex);
ta()()(i1, i2) = i;
ta()()(i2, i1) = -i;
ta()()(i1 + nsp, i2 + nsp) = i;
ta()()(i2 + nsp, i1 + nsp) = -i;
ta = ta * nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorCtype(int cIndex, iGroupMatrix<cplx> &ta) {
// ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
const int nsp=ncolour/2;
int i1, i2;
ta = Zero();
RealD nrm = 1 / (2 * std::sqrt(2));
su2SubGroupIndex(i1, i2, cIndex);
ta()()(i1, i2 + nsp) = 1;
ta()()(i2, i1 + nsp) = 1;
ta()()(i1 + nsp, i2) = 1;
ta()()(i2 + nsp, i1) = 1;
ta = ta * nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorDtype(int dIndex, iGroupMatrix<cplx> &ta) {
// ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i / 2 sqrt(2)
const int nsp=ncolour/2;
int i1, i2;
ta = Zero();
cplx i(0.0, 1.0);
RealD nrm = 1 / (2 * std::sqrt(2));
su2SubGroupIndex(i1, i2, dIndex);
ta()()(i1, i2 + nsp) = i;
ta()()(i2, i1 + nsp) = i;
ta()()(i1 + nsp, i2) = -i;
ta()()(i2 + nsp, i1) = -i;
ta = ta * nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorWtype(int wIndex, iGroupMatrix<cplx> &ta) {
// ta(i,i+N) = ta(i+N,i) = 1/2
const int nsp=ncolour/2;
ta = Zero();
RealD nrm = 1.0 / 2; // check
ta()()(wIndex, wIndex + nsp) = 1;
ta()()(wIndex + nsp, wIndex) = 1;
ta = ta * nrm;
}
template <class cplx, ONLY_IF_Sp>
static void generatorZtype(int zIndex, iGroupMatrix<cplx> &ta) {
// ta(i,i+N) = - ta(i+N,i) = i/2
const int nsp=ncolour/2;
ta = Zero();
RealD nrm = 1.0 / 2; // check
cplx i(0.0, 1.0);
ta()()(zIndex, zIndex + nsp) = i;
ta()()(zIndex + nsp, zIndex) = -i;
ta = ta * nrm;
}
////////////////////////////////////////////////////////////////////////
// Map a su2 subgroup number to the pair of rows that are non zero
////////////////////////////////////////////////////////////////////////
template <ONLY_IF_Sp>
static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::Sp) {
const int nsp=ncolour/2;
assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
int spare = su2_index;
for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
spare = spare - (nsp - 1 - i1); // remove the Nc-1-i1 terms
}
i2 = i1 + 1 + spare;
}
static void testGenerators(GroupName::Sp) {
Matrix ta;
Matrix tb;
std::cout << GridLogMessage
<< "Fundamental - Checking trace ta tb is 0.5 delta_ab "
<< std::endl;
for (int a = 0; a < AlgebraDimension; a++) {
for (int b = 0; b < AlgebraDimension; b++) {
generator(a, ta);
generator(b, tb);
Complex tr = TensorRemove(trace(ta * tb));
std::cout << GridLogMessage << "(" << a << "," << b << ") = " << tr
<< std::endl;
if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
if (a != b) assert(abs(tr) < 1.0e-6);
}
}
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
<< std::endl;
for (int a = 0; a < AlgebraDimension; a++) {
generator(a, ta);
std::cout << GridLogMessage << a << std::endl;
assert(norm2(ta - adj(ta)) < 1.0e-6);
}
std::cout << GridLogMessage << std::endl;
std::cout << GridLogMessage << "Fundamental - Checking if traceless"
<< std::endl;
for (int a = 0; a < AlgebraDimension; a++) {
generator(a, ta);
Complex tr = TensorRemove(trace(ta));
std::cout << GridLogMessage << a << std::endl;
assert(abs(tr) < 1.0e-6);
}
}
template <int N>
static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
return ProjectOnSpGroup(Umu);
}
template <class vtype>
accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::Sp) {
return ProjectOnSpGroup(r);
}
template <class vtype, int N>
accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::Sp) {
return ProjectOnSpGroup(r);
}
template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::Sp) {
return ProjectOnSpGroup(arg);
}
template <typename LatticeMatrixType>
static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
out = SpTa(in);
}
public:
template <ONLY_IF_Sp>
static void Omega(LatticeColourMatrixD &in) {
const int nsp=ncolour/2;
LatticeColourMatrixD OmegaLatt(in.Grid());
LatticeColourMatrixD identity(in.Grid());
ColourMatrix Omega;
OmegaLatt = Zero();
Omega = Zero();
identity = 1.;
for (int i = 0; i < nsp; i++) {
Omega()()(i, nsp + i) = 1.;
Omega()()(nsp + i, i) = -1;
}
OmegaLatt = OmegaLatt + (identity * Omega);
in = OmegaLatt;
}