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James H.'s code for general size Wilson loops
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@ -6,10 +6,12 @@
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Copyright (C) 2015
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Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: neo <cossu@post.kek.jp>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: neo <cossu@post.kek.jp>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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Author: James Harrison <J.Harrison@soton.ac.uk>
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Author: Antonin Portelli <antonin.portelli@me.com>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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@ -645,6 +647,184 @@ static void StapleMult(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
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}
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}
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}
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//////////////////////////////////////////////////
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// Wilson loop of size (R1, R2), oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void wilsonLoop(GaugeMat &wl, const std::vector<GaugeMat> &U,
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const int Rmu, const int Rnu,
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const int mu, const int nu) {
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wl = U[nu];
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for(int i = 0; i < Rnu-1; i++){
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wl = Gimpl::CovShiftForward(U[nu], nu, wl);
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}
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for(int i = 0; i < Rmu; i++){
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wl = Gimpl::CovShiftForward(U[mu], mu, wl);
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}
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for(int i = 0; i < Rnu; i++){
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wl = Gimpl::CovShiftBackward(U[nu], nu, wl);
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}
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for(int i = 0; i < Rmu; i++){
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wl = Gimpl::CovShiftBackward(U[mu], mu, wl);
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}
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}
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//////////////////////////////////////////////////
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// trace of Wilson Loop oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void traceWilsonLoop(LatticeComplex &wl,
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const std::vector<GaugeMat> &U,
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const int Rmu, const int Rnu,
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const int mu, const int nu) {
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GaugeMat sp(U[0]._grid);
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wilsonLoop(sp, U, Rmu, Rnu, mu, nu);
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wl = trace(sp);
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}
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//////////////////////////////////////////////////
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// sum over all planes of Wilson loop
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//////////////////////////////////////////////////
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static void siteWilsonLoop(LatticeComplex &Wl,
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const std::vector<GaugeMat> &U,
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const int R1, const int R2) {
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LatticeComplex siteWl(U[0]._grid);
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Wl = zero;
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for (int mu = 1; mu < U[0]._grid->_ndimension; mu++) {
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for (int nu = 0; nu < mu; nu++) {
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traceWilsonLoop(siteWl, U, R1, R2, mu, nu);
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Wl = Wl + siteWl;
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traceWilsonLoop(siteWl, U, R2, R1, mu, nu);
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Wl = Wl + siteWl;
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}
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}
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}
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//////////////////////////////////////////////////
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// sum over planes of Wilson loop with length R1
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// in the time direction
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//////////////////////////////////////////////////
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static void siteTimelikeWilsonLoop(LatticeComplex &Wl,
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const std::vector<GaugeMat> &U,
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const int R1, const int R2) {
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LatticeComplex siteWl(U[0]._grid);
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int ndim = U[0]._grid->_ndimension;
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Wl = zero;
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for (int nu = 0; nu < ndim - 1; nu++) {
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traceWilsonLoop(siteWl, U, R1, R2, ndim-1, nu);
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Wl = Wl + siteWl;
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}
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}
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//////////////////////////////////////////////////
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// sum Wilson loop over all planes orthogonal to the time direction
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//////////////////////////////////////////////////
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static void siteSpatialWilsonLoop(LatticeComplex &Wl,
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const std::vector<GaugeMat> &U,
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const int R1, const int R2) {
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LatticeComplex siteWl(U[0]._grid);
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Wl = zero;
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for (int mu = 1; mu < U[0]._grid->_ndimension - 1; mu++) {
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for (int nu = 0; nu < mu; nu++) {
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traceWilsonLoop(siteWl, U, R1, R2, mu, nu);
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Wl = Wl + siteWl;
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traceWilsonLoop(siteWl, U, R2, R1, mu, nu);
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Wl = Wl + siteWl;
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}
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}
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of Wilson loop
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//////////////////////////////////////////////////
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static Real sumWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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std::vector<GaugeMat> U(4, Umu._grid);
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for (int mu = 0; mu < Umu._grid->_ndimension; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
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}
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LatticeComplex Wl(Umu._grid);
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siteWilsonLoop(Wl, U, R1, R2);
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TComplex Tp = sum(Wl);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of timelike Wilson loop
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//////////////////////////////////////////////////
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static Real sumTimelikeWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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std::vector<GaugeMat> U(4, Umu._grid);
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for (int mu = 0; mu < Umu._grid->_ndimension; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
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}
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LatticeComplex Wl(Umu._grid);
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siteTimelikeWilsonLoop(Wl, U, R1, R2);
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TComplex Tp = sum(Wl);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of spatial Wilson loop
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//////////////////////////////////////////////////
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static Real sumSpatialWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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std::vector<GaugeMat> U(4, Umu._grid);
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for (int mu = 0; mu < Umu._grid->_ndimension; mu++) {
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U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
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}
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LatticeComplex Wl(Umu._grid);
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siteSpatialWilsonLoop(Wl, U, R1, R2);
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TComplex Tp = sum(Wl);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of Wilson loop
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//////////////////////////////////////////////////
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static Real avgWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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int ndim = Umu._grid->_ndimension;
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Real sumWl = sumWilsonLoop(Umu, R1, R2);
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Real vol = Umu._grid->gSites();
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Real faces = 1.0 * ndim * (ndim - 1);
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return sumWl / vol / faces / Nc; // Nc dependent... FIXME
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of timelike Wilson loop
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//////////////////////////////////////////////////
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static Real avgTimelikeWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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int ndim = Umu._grid->_ndimension;
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Real sumWl = sumTimelikeWilsonLoop(Umu, R1, R2);
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Real vol = Umu._grid->gSites();
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Real faces = 1.0 * (ndim - 1);
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return sumWl / vol / faces / Nc; // Nc dependent... FIXME
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of spatial Wilson loop
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//////////////////////////////////////////////////
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static Real avgSpatialWilsonLoop(const GaugeLorentz &Umu,
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const int R1, const int R2) {
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int ndim = Umu._grid->_ndimension;
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Real sumWl = sumSpatialWilsonLoop(Umu, R1, R2);
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Real vol = Umu._grid->gSites();
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Real faces = 1.0 * (ndim - 1) * (ndim - 2);
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return sumWl / vol / faces / Nc; // Nc dependent... FIXME
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}
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};
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typedef WilsonLoops<PeriodicGimplR> ColourWilsonLoops;
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