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2AS for every Nc!

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This commit is contained in:
Alessandro Lupo 2023-05-17 20:22:05 +01:00
parent 55f9cce577
commit 932c783fbf
3 changed files with 131 additions and 24 deletions
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10
Grid/qcd/utils/GaugeGroupTwoIndex.h
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@ -78,7 +78,7 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
template <class cplx>
static void base(int Index, iGroupMatrix<cplx> &eij) {
// returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
assert(Index < NumGenerators);
assert(Index < Dimension);
eij = Zero();
// for the linearisation of the 2 indexes
@ -89,9 +89,10 @@ class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
for (int i = 1; i < ncolour; i++) {
for (int j = 0; j < i; j++) {
a[counter][0] = i;
j = i == ngroup ? j + 1
: j; // this will only ever trigger for Sp because
// ngroup == ncolour is out of range for SU
if (j==0 && ngroup == ncolour/2 && i==ngroup+j) {
//std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
j = j+1;
}
a[counter][1] = j;
counter++;
}
@ -320,6 +321,7 @@ typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;

110
tests/sp2n/Test_2as_base.cc Normal file
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@ -0,0 +1,110 @@
#include <Grid/Grid.h>
#define verbose 0
using namespace Grid;
int main(int argc, char** argv) {
Grid_init(&argc, &argv);
const int this_nc = 4;
const int this_n = this_nc/2;
const int this_irrep_dim = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension;
const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupMatrix<Complex> Matrix;
typedef Sp_TwoIndex<this_nc, AntiSymmetric>::iGroupTwoIndexMatrix<Complex> ASMatrix;
Matrix Omega;
Matrix eij_a;
Matrix eij_b;
Matrix eij_c;
Matrix e_sum;
Omega = Zero();
for (int i = 0; i < this_n; i++)
{
Omega()()(i, this_n + i) = 1.;
Omega()()(this_n + i, i) = -1;
}
std::cout << "Omega " << Omega << std::endl;
RealD realA;
RealD realB;
std::cout << GridLogMessage << "2as dimension is " << this_irrep_dim << std::endl;
std::cout << GridLogMessage << "algebra dimension is " << this_algebra_dim << std::endl;
realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
realB = Sp<this_nc>::Dimension*Sp<this_nc>::Dimension;
assert ( realA == realB);
std::cout << GridLogMessage << "checking base is antisymmetric " << std::endl;
for (int a=0; a < this_irrep_dim; a++)
{
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_c);
e_sum = eij_c + transpose(eij_c);
std::cout << GridLogMessage << "e_ab + e_ab^T " << norm2(e_sum) << std::endl;
assert(norm2(e_sum) < 1e-8);
}
std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
for (int a=0; a < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; a++) {
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij_a);
realA = norm2(trace(Omega*eij_a));
std::cout << GridLogMessage << "Omega trace for (ab) = " << a << std::endl;
assert(realA == 0);
for (int b=0; b < Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension; b++) {
Sp_TwoIndex<this_nc, AntiSymmetric>::base(b, eij_b);
auto d_ab = TensorRemove(trace(eij_a * eij_b));
#if verbose
std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
#endif
std::cout << GridLogMessage << "Orthonormality for (ab) = " << a << std::endl;
if (a==b) {
assert(real(d_ab)+1 < 1e-8);
assert(imag(d_ab) < 1e-8);
} else {
assert(real(d_ab) < 1e-8);
assert(imag(d_ab) < 1e-8);
}
}
}
int sum = 0;
int sum_im = 0;
Vector<Matrix> ta_fund(this_algebra_dim);
Vector<Matrix> eij(this_irrep_dim);
Matrix tmp_l;
Matrix tmp_r;
for (int n = 0; n < this_algebra_dim; n++)
{
Sp<this_nc>::generator(n, ta_fund[n]);
}
for (int a = 0; a < this_irrep_dim; a++)
{
Sp_TwoIndex<this_nc, AntiSymmetric>::base(a, eij[a]);
}
for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
{
Complex iTr;
sum = 0;
sum_im = 0;
std::cout << GridLogMessage << "generator number " << gen_id << std::endl;
for (int a = 0; a < this_irrep_dim; a++)
{
tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
#if verbose
std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
#endif
std::cout << GridLogMessage << " as_indx = " << a << " Tr(sum) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
sum += real(TensorRemove(trace(tmp_l+tmp_r)));
sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
}
std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
assert ( sum < 1e-8) ;
assert ( sum_im < 1e-8) ;
}
Grid_finalize();
}

23
tests/sp2n/Test_sp2n_lie_gen.cc
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@ -7,7 +7,7 @@ int main(int argc, char** argv) {
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(2)" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(2) (print and test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
@ -16,7 +16,7 @@ int main(int argc, char** argv) {
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(4)" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(4) (print and test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
@ -25,47 +25,42 @@ int main(int argc, char** argv) {
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(6)" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(6) (test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
Sp6::printGenerators();
Sp6::testGenerators();
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(8)" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(8) (test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
Sp8::printGenerators();
Sp8::testGenerators();
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndex AntiSymmetric" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(4) TwoIndexAS (test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
Sp4TwoIndexAntiSymm::printGenerators();
Sp4TwoIndexAntiSymm::testGenerators();
Sp_TwoIndex<4, AntiSymmetric>:::testGenerators();
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndex AntiSymmetric" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(6) TwoIndexAS (test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
SU_TwoIndex<6, AntiSymmetric>::printGenerators();
SU_TwoIndex<6, AntiSymmetric>::testGenerators();
Sp_TwoIndex<6, AntiSymmetric>::testGenerators();
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndex AntiSymmetric" << std::endl;
std::cout << GridLogMessage << "* Generators for Sp(8) TwoIndexAS (test)" << std::endl;
std::cout << GridLogMessage << "*********************************************"
<< std::endl;
Sp_TwoIndex<8, AntiSymmetric>::printGenerators();
Sp_TwoIndex<8, AntiSymmetric>::testGenerators();
Grid_finalize();