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Grid/lib/qcd/utils/WilsonLoops.h
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./lib/qcd/utils/WilsonLoops.h
Copyright (C) 2015
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>
Author: paboyle <paboyle@ph.ed.ac.uk>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
See the full license in the file "LICENSE" in the top level distribution
directory
*************************************************************************************/
/* END LEGAL */
#ifndef QCD_UTILS_WILSON_LOOPS_H
#define QCD_UTILS_WILSON_LOOPS_H
NAMESPACE_BEGIN(Grid);
// Common wilson loop observables
template <class Gimpl> class WilsonLoops : public Gimpl {
public:
INHERIT_GIMPL_TYPES(Gimpl);
typedef typename Gimpl::GaugeLinkField GaugeMat;
typedef typename Gimpl::GaugeField GaugeLorentz;
//////////////////////////////////////////////////
// directed plaquette oriented in mu,nu plane
//////////////////////////////////////////////////
static void dirPlaquette(GaugeMat &plaq, const std::vector<GaugeMat> &U,
const int mu, const int nu) {
// Annoyingly, must use either scope resolution to find dependent base
// class,
// or this-> ; there is no "this" in a static method. This forces explicit
// Gimpl scope
// resolution throughout the usage in this file, and rather defeats the
// purpose of deriving
// from Gimpl.
/*
plaq = Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftBackward(
U[nu], nu, Gimpl::CovShiftForward(U[mu], mu, U[nu])));
*/
// _
//|< _|
plaq = Gimpl::CovShiftForward(U[mu],mu,
Gimpl::CovShiftForward(U[nu],nu,
Gimpl::CovShiftBackward(U[mu],mu,
Gimpl::CovShiftIdentityBackward(U[nu], nu))));
}
//////////////////////////////////////////////////
// trace of directed plaquette oriented in mu,nu plane
//////////////////////////////////////////////////
static void traceDirPlaquette(ComplexField &plaq,
const std::vector<GaugeMat> &U, const int mu,
const int nu) {
GaugeMat sp(U[0]._grid);
dirPlaquette(sp, U, mu, nu);
plaq = trace(sp);
}
//////////////////////////////////////////////////
// sum over all planes of plaquette
//////////////////////////////////////////////////
static void sitePlaquette(ComplexField &Plaq,
const std::vector<GaugeMat> &U) {
ComplexField sitePlaq(U[0]._grid);
Plaq = zero;
for (int mu = 1; mu < Nd; mu++) {
for (int nu = 0; nu < mu; nu++) {
traceDirPlaquette(sitePlaq, U, mu, nu);
Plaq = Plaq + sitePlaq;
}
}
}
//////////////////////////////////////////////////
// sum over all x,y,z,t and over all planes of plaquette
//////////////////////////////////////////////////
static RealD sumPlaquette(const GaugeLorentz &Umu) {
std::vector<GaugeMat> U(Nd, Umu._grid);
// inefficient here
for (int mu = 0; mu < Nd; mu++) {
U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
}
ComplexField Plaq(Umu._grid);
sitePlaquette(Plaq, U);
auto Tp = sum(Plaq);
auto p = TensorRemove(Tp);
return p.real();
}
//////////////////////////////////////////////////
// average over all x,y,z,t and over all planes of plaquette
//////////////////////////////////////////////////
static RealD avgPlaquette(const GaugeLorentz &Umu) {
RealD sumplaq = sumPlaquette(Umu);
double vol = Umu._grid->gSites();
double faces = (1.0 * Nd * (Nd - 1)) / 2.0;
return sumplaq / vol / faces / Nc; // Nd , Nc dependent... FIXME
}
//////////////////////////////////////////////////
// average over traced single links
//////////////////////////////////////////////////
static RealD linkTrace(const GaugeLorentz &Umu) {
std::vector<GaugeMat> U(Nd, Umu._grid);
ComplexField Tr(Umu._grid);
Tr = zero;
for (int mu = 0; mu < Nd; mu++) {
U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
Tr = Tr + trace(U[mu]);
}
auto Tp = sum(Tr);
auto p = TensorRemove(Tp);
double vol = Umu._grid->gSites();
return p.real() / vol / 4.0 / 3.0;
};
//////////////////////////////////////////////////
// the sum over all staples on each site in direction mu,nu
//////////////////////////////////////////////////
static void Staple(GaugeMat &staple, const GaugeLorentz &Umu, int mu,
int nu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
U[d] = PeekIndex<LorentzIndex>(Umu, d);
}
staple = zero;
if (nu != mu) {
// mu
// ^
// |__> nu
// __
// |
// __|
//
staple += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftIdentityBackward(U[nu], nu))),
mu);
// __
// |
// |__
//
//
staple += Gimpl::ShiftStaple(
Gimpl::CovShiftBackward(U[nu], nu,
Gimpl::CovShiftBackward(U[mu], mu, U[nu])),
mu);
}
}
// For the force term
static void StapleMult(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
// this operation is taking too much time
U[d] = PeekIndex<LorentzIndex>(Umu, d);
}
staple = zero;
GaugeMat tmp1(grid);
GaugeMat tmp2(grid);
for (int nu = 0; nu < Nd; nu++) {
if (nu != mu) {
// this is ~10% faster than the Staple
tmp1 = Cshift(U[nu], mu, 1);
tmp2 = Cshift(U[mu], nu, 1);
staple += tmp1* adj(U[nu]*tmp2);
tmp2 = adj(U[mu]*tmp1)*U[nu];
staple += Cshift(tmp2, nu, -1);
}
}
staple = U[mu]*staple;
}
//////////////////////////////////////////////////
// the sum over all staples on each site
//////////////////////////////////////////////////
static void Staple(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
U[d] = PeekIndex<LorentzIndex>(Umu, d);
}
staple = zero;
for (int nu = 0; nu < Nd; nu++) {
if (nu != mu) {
// mu
// ^
// |__> nu
// __
// |
// __|
//
staple += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftIdentityBackward(U[nu], nu))),
mu);
// __
// |
// |__
//
//
staple += Gimpl::ShiftStaple(
Gimpl::CovShiftBackward(U[nu], nu,
Gimpl::CovShiftBackward(U[mu], mu, U[nu])), mu);
}
}
}
//////////////////////////////////////////////////
// the sum over all staples on each site in direction mu,nu, upper part
//////////////////////////////////////////////////
static void StapleUpper(GaugeMat &staple, const GaugeLorentz &Umu, int mu,
int nu) {
if (nu != mu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
U[d] = PeekIndex<LorentzIndex>(Umu, d);// some redundant copies
}
// mu
// ^
// |__> nu
// __
// |
// __|
//
staple = Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftIdentityBackward(U[nu], nu))),
mu);
}
}
//////////////////////////////////////////////////
// the sum over all staples on each site in direction mu,nu, lower part
//////////////////////////////////////////////////
static void StapleLower(GaugeMat &staple, const GaugeLorentz &Umu, int mu,
int nu) {
if (nu != mu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
U[d] = PeekIndex<LorentzIndex>(Umu, d);// some redundant copies
}
// mu
// ^
// |__> nu
// __
// |
// |__
//
//
staple = Gimpl::ShiftStaple(
Gimpl::CovShiftBackward(U[nu], nu,
Gimpl::CovShiftBackward(U[mu], mu, U[nu])), mu);
}
}
//////////////////////////////////////////////////////
// Field Strength
//////////////////////////////////////////////////////
static void FieldStrength(GaugeMat &FS, const GaugeLorentz &Umu, int mu, int nu){
// Fmn +--<--+ Ut +--<--+
// | | | |
// (x)+-->--+ +-->--+(x)
// | | | |
// +--<--+ +--<--+
GaugeMat Vup(Umu._grid), Vdn(Umu._grid);
StapleUpper(Vup, Umu, mu, nu);
StapleLower(Vdn, Umu, mu, nu);
GaugeMat v = Vup - Vdn;
GaugeMat u = PeekIndex<LorentzIndex>(Umu, mu); // some redundant copies
GaugeMat vu = v*u;
FS = 0.25*Ta(u*v + Cshift(vu, mu, -1));
}
static Real TopologicalCharge(GaugeLorentz &U){
// 4d topological charge
assert(Nd==4);
// Bx = -iF(y,z), By = -iF(z,y), Bz = -iF(x,y)
GaugeMat Bx(U._grid), By(U._grid), Bz(U._grid);
FieldStrength(Bx, U, Ydir, Zdir);
FieldStrength(By, U, Zdir, Xdir);
FieldStrength(Bz, U, Xdir, Ydir);
// Ex = -iF(t,x), Ey = -iF(t,y), Ez = -iF(t,z)
GaugeMat Ex(U._grid), Ey(U._grid), Ez(U._grid);
FieldStrength(Ex, U, Tdir, Xdir);
FieldStrength(Ey, U, Tdir, Ydir);
FieldStrength(Ez, U, Tdir, Zdir);
double coeff = 8.0/(32.0*M_PI*M_PI);
ComplexField qfield = coeff*trace(Bx*Ex + By*Ey + Bz*Ez);
auto Tq = sum(qfield);
return TensorRemove(Tq).real();
}
//////////////////////////////////////////////////////
// Similar to above for rectangle is required
//////////////////////////////////////////////////////
static void dirRectangle(GaugeMat &rect, const std::vector<GaugeMat> &U,
const int mu, const int nu) {
rect = Gimpl::CovShiftForward(
U[mu], mu, Gimpl::CovShiftForward(U[mu], mu, U[nu])) * // ->->|
adj(Gimpl::CovShiftForward(
U[nu], nu, Gimpl::CovShiftForward(U[mu], mu, U[mu])));
rect = rect +
Gimpl::CovShiftForward(
U[mu], mu, Gimpl::CovShiftForward(U[nu], nu, U[nu])) * // ->||
adj(Gimpl::CovShiftForward(
U[nu], nu, Gimpl::CovShiftForward(U[nu], nu, U[mu])));
}
static void traceDirRectangle(ComplexField &rect,
const std::vector<GaugeMat> &U, const int mu,
const int nu) {
GaugeMat sp(U[0]._grid);
dirRectangle(sp, U, mu, nu);
rect = trace(sp);
}
static void siteRectangle(ComplexField &Rect,
const std::vector<GaugeMat> &U) {
ComplexField siteRect(U[0]._grid);
Rect = zero;
for (int mu = 1; mu < Nd; mu++) {
for (int nu = 0; nu < mu; nu++) {
traceDirRectangle(siteRect, U, mu, nu);
Rect = Rect + siteRect;
}
}
}
//////////////////////////////////////////////////
// sum over all x,y,z,t and over all planes of plaquette
//////////////////////////////////////////////////
static RealD sumRectangle(const GaugeLorentz &Umu) {
std::vector<GaugeMat> U(Nd, Umu._grid);
for (int mu = 0; mu < Nd; mu++) {
U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
}
ComplexField Rect(Umu._grid);
siteRectangle(Rect, U);
auto Tp = sum(Rect);
auto p = TensorRemove(Tp);
return p.real();
}
//////////////////////////////////////////////////
// average over all x,y,z,t and over all planes of plaquette
//////////////////////////////////////////////////
static RealD avgRectangle(const GaugeLorentz &Umu) {
RealD sumrect = sumRectangle(Umu);
double vol = Umu._grid->gSites();
double faces = (1.0 * Nd * (Nd - 1)); // 2 distinct orientations summed
return sumrect / vol / faces / Nc; // Nd , Nc dependent... FIXME
}
//////////////////////////////////////////////////
// the sum over all staples on each site
//////////////////////////////////////////////////
static void RectStapleDouble(GaugeMat &U2, const GaugeMat &U, int mu) {
U2 = U * Cshift(U, mu, 1);
}
////////////////////////////////////////////////////////////////////////////
// Hop by two optimisation strategy does not work nicely with Gparity. (could
// do,
// but need to track two deep where cross boundary and apply a conjugation).
// Must differentiate this in Gimpl, and use Gimpl::isPeriodicGaugeField to do
// so .
////////////////////////////////////////////////////////////////////////////
static void RectStapleOptimised(GaugeMat &Stap, std::vector<GaugeMat> &U2,
std::vector<GaugeMat> &U, int mu) {
Stap = zero;
GridBase *grid = U[0]._grid;
GaugeMat Staple2x1(grid);
GaugeMat tmp(grid);
for (int nu = 0; nu < Nd; nu++) {
if (nu != mu) {
// Up staple ___ ___
// | |
tmp = Cshift(adj(U[nu]), nu, -1);
tmp = adj(U2[mu]) * tmp;
tmp = Cshift(tmp, mu, -2);
Staple2x1 = Gimpl::CovShiftForward(U[nu], nu, tmp);
// Down staple
// |___ ___|
//
tmp = adj(U2[mu]) * U[nu];
Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Cshift(tmp, mu, -2));
// ___ ___
// | ___|
// |___ ___|
//
Stap += Cshift(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
// ___ ___
// |___ |
// |___ ___|
//
// tmp= Staple2x1* Cshift(U[mu],mu,-2);
// Stap+= Cshift(tmp,mu,1) ;
Stap += Cshift(Staple2x1, mu, 1) * Cshift(U[mu], mu, -1);
;
// --
// | |
//
// | |
tmp = Cshift(adj(U2[nu]), nu, -2);
tmp = Gimpl::CovShiftBackward(U[mu], mu, tmp);
tmp = U2[nu] * Cshift(tmp, nu, 2);
Stap += Cshift(tmp, mu, 1);
// | |
//
// | |
// --
tmp = Gimpl::CovShiftBackward(U[mu], mu, U2[nu]);
tmp = adj(U2[nu]) * tmp;
tmp = Cshift(tmp, nu, -2);
Stap += Cshift(tmp, mu, 1);
}
}
}
static void RectStaple(GaugeMat &Stap, const GaugeLorentz &Umu, int mu) {
RectStapleUnoptimised(Stap, Umu, mu);
}
static void RectStaple(const GaugeLorentz &Umu, GaugeMat &Stap,
std::vector<GaugeMat> &U2, std::vector<GaugeMat> &U,
int mu) {
if (Gimpl::isPeriodicGaugeField()) {
RectStapleOptimised(Stap, U2, U, mu);
} else {
RectStapleUnoptimised(Stap, Umu, mu);
}
}
static void RectStapleUnoptimised(GaugeMat &Stap, const GaugeLorentz &Umu,
int mu) {
GridBase *grid = Umu._grid;
std::vector<GaugeMat> U(Nd, grid);
for (int d = 0; d < Nd; d++) {
U[d] = PeekIndex<LorentzIndex>(Umu, d);
}
Stap = zero;
for (int nu = 0; nu < Nd; nu++) {
if (nu != mu) {
// __ ___
// | __ |
//
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[mu], mu,
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu,
Gimpl::CovShiftBackward(
U[mu], mu,
Gimpl::CovShiftIdentityBackward(U[nu], nu))))),
mu);
// __
// |__ __ |
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[mu], mu,
Gimpl::CovShiftBackward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftBackward(U[mu], mu, U[nu])))),
mu);
// __
// |__ __ |
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftBackward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftForward(U[nu], nu, U[mu])))),
mu);
// __ ___
// |__ |
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftBackward(U[nu], nu, U[mu])))),
mu);
// --
// | |
//
// | |
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftForward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu,
Gimpl::CovShiftBackward(
U[nu], nu,
Gimpl::CovShiftIdentityBackward(U[nu], nu))))),
mu);
// | |
//
// | |
// --
Stap += Gimpl::ShiftStaple(
Gimpl::CovShiftBackward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[nu], nu,
Gimpl::CovShiftBackward(
U[mu], mu, Gimpl::CovShiftForward(U[nu], nu, U[nu])))),
mu);
}
}
}
};
typedef WilsonLoops<PeriodicGimplR> ColourWilsonLoops;
typedef WilsonLoops<PeriodicGimplR> U1WilsonLoops;
typedef WilsonLoops<PeriodicGimplR> SU2WilsonLoops;
typedef WilsonLoops<PeriodicGimplR> SU3WilsonLoops;
NAMESPACE_END(Grid);
#endif
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