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QedFVol: calculate square Wilson loops up to 10x10

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This commit is contained in:
James Harrison 2016-11-14 18:23:04 +00:00
parent d49e502f53
commit a71b69389b
1 changed files with 14 additions and 60 deletions
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74
programs/qed-fvol/qed-fvol.cc
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@ -64,75 +64,29 @@ int main(int argc, char *argv[])
EmField a(&grid); EmField a(&grid);
EmField expA(&grid); EmField expA(&grid);
Real avgPlaqAexp, avgWl2x2Aexp, avgWl2x2Aexp_time, avgWl2x2Aexp_space; Real wlA, logWlA;
pRNG.SeedRandomDevice(); pRNG.SeedRandomDevice();
photon.StochasticField(a, pRNG); photon.StochasticField(a, pRNG);
// Exponentiate photon field // Exponentiate photon field
Complex imag_unit(0, 1); Complex imag_unit(0, 1);
expA = exp(imag_unit*0.5*(a+conjugate(a))); expA = exp(imag_unit*a);
// Calculate plaquette from photon field // Calculate Wilson loops
EmComp plaqA(&grid); for(int i=1; i<=10; i++){
EmComp wlA(&grid); LOG(Message) << i << 'x' << i << " Wilson loop" << std::endl;
EmComp tmp(&grid); wlA = NewWilsonLoops<QedPeriodicGimplR>::avgWilsonLoop(expA, i, i) * 3;
std::vector<EmComp> a_comp(4, &grid); logWlA = -2*log(wlA);
LOG(Message) << "-2log(W) average: " << logWlA << std::endl;
for (int dir = 0; dir < Nd; dir++) { wlA = NewWilsonLoops<QedPeriodicGimplR>::avgTimelikeWilsonLoop(expA, i, i) * 3;
a_comp[dir] = PeekIndex<LorentzIndex>(a, dir); logWlA = -2*log(wlA);
LOG(Message) << "-2log(W) timelike: " << logWlA << std::endl;
wlA = NewWilsonLoops<QedPeriodicGimplR>::avgSpatialWilsonLoop(expA, i, i) * 3;
logWlA = -2*log(wlA);
LOG(Message) << "-2log(W) spatial: " << logWlA << std::endl;
} }
plaqA = zero;
wlA = zero;
for(int mu = 1; mu < Nd; mu++) {
for(int nu = 0; nu < mu; nu++) {
tmp = a_comp[mu] + Cshift(a_comp[nu], mu, 1) - Cshift(a_comp[mu], nu, 1) - a_comp[nu];
plaqA = plaqA + cos(tmp);
tmp = a_comp[mu] + Cshift(a_comp[mu], mu, 1)
+ Cshift(a_comp[nu], mu, 2) + Cshift(Cshift(a_comp[nu], mu, 2), nu, 1)
- Cshift(Cshift(a_comp[mu], nu, 2), mu, 1) - Cshift(a_comp[mu], nu, 2)
- Cshift(a_comp[nu], nu, 1) - a_comp[nu];
wlA = wlA + cos(tmp);
}
}
Real vol = grid.gSites();
Real faces = (1.0 * Nd * (Nd - 1)) / 2.0;
Complex avgPlaqA = sum(trace(plaqA));
avgPlaqA = avgPlaqA / vol / faces;
Complex avgWlA = sum(trace(wlA));
avgWlA = avgWlA / vol / faces;
TComplex tplaqsite;
LatticeComplex plaqtrace = trace(plaqA);
std::vector<int> site0 = {0,0,0,0};
peekSite(tplaqsite, plaqtrace, site0);
Complex plaqsite = TensorRemove(tplaqsite);
// Calculate plaquette from exponentiated photon field
avgPlaqAexp = NewWilsonLoops<QedPeriodicGimplR>::avgPlaquette(expA);
avgWl2x2Aexp = NewWilsonLoops<QedPeriodicGimplR>::avgWilsonLoop(expA, 2, 2);
avgWl2x2Aexp_time = NewWilsonLoops<QedPeriodicGimplR>::avgTimelikeWilsonLoop(expA, 2, 2);
avgWl2x2Aexp_space = NewWilsonLoops<QedPeriodicGimplR>::avgSpatialWilsonLoop(expA, 2, 2);
avgPlaqAexp = avgPlaqAexp*3;
avgWl2x2Aexp = avgWl2x2Aexp*3;
avgWl2x2Aexp_time = avgWl2x2Aexp_time*3;
avgWl2x2Aexp_space = avgWl2x2Aexp_space*3;
LOG(Message) << "Plaquette average (from A): " << avgPlaqA << std::endl;
LOG(Message) << "Plaquette average (from exp(A)): " << avgPlaqAexp << std::endl;
LOG(Message) << "2x2 Wilson Loop average (from A): " << avgWlA << std::endl;
LOG(Message) << "2x2 Wilson Loop average (from exp(A)): " << avgWl2x2Aexp << std::endl;
LOG(Message) << "2x2 Wilson Loop timelike average (from exp(A)): " << avgWl2x2Aexp_time << std::endl;
LOG(Message) << "2x2 Wilson Loop spatial average (from exp(A)): " << avgWl2x2Aexp_space << std::endl;
LOG(Message) << "Plaquette (one site): " << plaqsite / faces << std::endl;
// epilogue // epilogue
LOG(Message) << "Grid is finalizing now" << std::endl; LOG(Message) << "Grid is finalizing now" << std::endl;
Grid_finalize(); Grid_finalize();