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Added calculation of timeslice topological charge

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This commit is contained in:
Christopher Kelly 2022-01-20 14:29:07 -05:00
parent c4ac528126
commit adeba8059a
1 changed files with 41 additions and 9 deletions
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50
Grid/qcd/utils/WilsonLoops.h
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@ -485,7 +485,8 @@ public:
//Topological charge contribution from MxN Wilson loops
//cf https://arxiv.org/pdf/hep-lat/9701012.pdf Eq 6
static Real TopologicalChargeMxN(const GaugeLorentz &U, int M, int N){
//output is the charge by timeslice: sum over timeslices to obtain the total
static std::vector<Real> TimesliceTopologicalChargeMxN(const GaugeLorentz &U, int M, int N){
assert(Nd == 4);
std::vector<std::vector<GaugeMat*> > F(Nd,std::vector<GaugeMat*>(Nd,nullptr));
//Note F_numu = - F_munu
@ -513,9 +514,20 @@ public:
for(int mu=0;mu<Nd-1;mu++)
for(int nu=mu+1; nu<Nd; nu++)
delete F[mu][nu];
typedef typename ComplexField::scalar_object sobj;
std::vector<sobj> Tq;
sliceSum(fsum, Tq, Nd-1);
auto Tq = sum(fsum);
return TensorRemove(Tq).real();
std::vector<Real> out(Tq.size());
for(int t=0;t<Tq.size();t++) out[t] = TensorRemove(Tq[t]).real();
return out;
}
static Real TopologicalChargeMxN(const GaugeLorentz &U, int M, int N){
std::vector<Real> Tq = TimesliceTopologicalChargeMxN(U,M,N);
Real out(0);
for(int t=0;t<Tq.size();t++) out += Tq[t];
return out;
}
//Generate the contributions to the 5Li topological charge from Wilson loops of the following sizes
@ -525,12 +537,22 @@ public:
//1x2 : c3=(-64.+640.*c5)/45.
//1x3 : c4=1./5.-2.*c5
//3x3 : c5=1./20.
//Output array contains the loops in the above order
static std::vector<Real> TopologicalCharge5LiContributions(const GaugeLorentz &U){
//Output array outer index contains the loops in the above order
//Inner index is the time coordinate
static std::vector<std::vector<Real> > TimesliceTopologicalCharge5LiContributions(const GaugeLorentz &U){
static const int exts[5][2] = { {1,1}, {2,2}, {1,2}, {1,3}, {3,3} };
std::vector<std::vector<Real> > out(5);
for(int i=0;i<5;i++){
out[i] = TimesliceTopologicalChargeMxN(U,exts[i][0],exts[i][1]);
}
return out;
}
static std::vector<Real> TopologicalCharge5LiContributions(const GaugeLorentz &U){
static const int exts[5][2] = { {1,1}, {2,2}, {1,2}, {1,3}, {3,3} };
std::vector<Real> out(5);
std::cout << GridLogMessage << "Computing topological charge" << std::endl;
for(int i=0;i<5;i++){
for(int i=0;i<5;i++){
out[i] = TopologicalChargeMxN(U,exts[i][0],exts[i][1]);
std::cout << GridLogMessage << exts[i][0] << "x" << exts[i][1] << " Wilson loop contribution " << out[i] << std::endl;
}
@ -538,8 +560,8 @@ public:
}
//Compute the 5Li topological charge
static Real TopologicalCharge5Li(const GaugeLorentz &U){
std::vector<Real> loops = TopologicalCharge5LiContributions(U);
static std::vector<Real> TimesliceTopologicalCharge5Li(const GaugeLorentz &U){
std::vector<std::vector<Real> > loops = TimesliceTopologicalCharge5LiContributions(U);
double c5=1./20.;
double c4=1./5.-2.*c5;
@ -547,14 +569,24 @@ public:
double c2=(1-64.*c5)/9.;
double c1=(19.-55.*c5)/9.;
double Q = c1*loops[0] + c2*loops[1] + c3*loops[2] + c4*loops[3] + c5*loops[4];
int Lt = loops[0].size();
std::vector<Real> out(Lt,0.);
for(int t=0;t<Lt;t++)
out[t] += c1*loops[0][t] + c2*loops[1][t] + c3*loops[2][t] + c4*loops[3][t] + c5*loops[4][t];
return out;
}
static Real TopologicalCharge5Li(const GaugeLorentz &U){
std::vector<Real> Qt = TimesliceTopologicalCharge5Li(U);
Real Q = 0.;
for(int t=0;t<Qt.size();t++) Q += Qt[t];
std::cout << GridLogMessage << "5Li Topological charge: " << Q << std::endl;
return Q;
}
//////////////////////////////////////////////////////
// Similar to above for rectangle is required
//////////////////////////////////////////////////////