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5D free propagator for DWF and boundary conditions for free propagators
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Vera Guelpers
@ -13,6 +13,7 @@ Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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Author: Guido Cossu <guido.cossu@ed.ac.uk>
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Author: Andrew Lawson <andrew.lawson1991@gmail.com>
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Author: Vera Guelpers <V.M.Guelpers@soton.ac.uk>
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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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@ -563,7 +564,221 @@ void WilsonFermion5D<Impl>::DW(const FermionField &in, FermionField &out,int dag
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}
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template<class Impl>
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void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const FermionField &in, RealD mass)
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void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt_5d(FermionField &out,const FermionField &in, RealD mass,std::vector<double> twist)
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{
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// what type LatticeComplex
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GridBase *_grid = _FourDimGrid;
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GridBase *_5dgrid = _FiveDimGrid;
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conformable(_5dgrid,out._grid);
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FermionField PRsource(_5dgrid);
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FermionField PLsource(_5dgrid);
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FermionField buf1_4d(_grid);
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FermionField buf2_4d(_grid);
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FermionField GR(_5dgrid);
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FermionField GL(_5dgrid);
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FermionField bufL_4d(_grid);
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FermionField bufR_4d(_grid);
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unsigned int Ls = in._grid->_rdimensions[0];
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typedef typename FermionField::vector_type vector_type;
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typedef typename FermionField::scalar_type ScalComplex;
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typedef iSinglet<ScalComplex> Tcomplex;
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typedef Lattice<iSinglet<vector_type> > LatComplex;
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Gamma::Algebra Gmu [] = {
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Gamma::Algebra::GammaX,
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Gamma::Algebra::GammaY,
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Gamma::Algebra::GammaZ,
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Gamma::Algebra::GammaT
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};
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Gamma g5(Gamma::Algebra::Gamma5);
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std::vector<int> latt_size = _grid->_fdimensions;
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LatComplex sk(_grid); sk = zero;
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LatComplex sk2(_grid); sk2= zero;
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LatComplex W(_grid); W= zero;
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LatComplex a(_grid); a= zero;
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LatComplex one (_grid); one = ScalComplex(1.0,0.0);
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LatComplex cosha(_grid);
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LatComplex kmu(_grid);
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LatComplex Wea(_grid);
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LatComplex Wema(_grid);
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LatComplex sinha(_grid);
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LatComplex sinhaLs(_grid);
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LatComplex coshaLs(_grid);
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LatComplex A(_grid);
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LatComplex F(_grid);
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LatComplex App(_grid);
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LatComplex Amm(_grid);
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LatComplex Bpp(_grid);
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LatComplex Bmm(_grid);
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LatComplex ABpm(_grid); //Apm=Amp=Bpm=Bmp
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LatComplex signW(_grid);
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ScalComplex ci(0.0,1.0);
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for(int mu=0;mu<Nd;mu++) {
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LatticeCoordinate(kmu,mu);
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RealD TwoPiL = M_PI * 2.0/ latt_size[mu];
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kmu = TwoPiL * kmu;
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kmu = kmu + TwoPiL * one * twist[mu];//momentum for twisted boundary conditions
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sk2 = sk2 + 2.0*sin(kmu*0.5)*sin(kmu*0.5);
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sk = sk + sin(kmu) *sin(kmu);
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}
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W = one - M5 + sk2;
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////////////////////////////////////////////
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// Cosh alpha -> alpha
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////////////////////////////////////////////
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cosha = (one + W*W + sk) / (abs(W)*2.0);
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// FIXME Need a Lattice acosh
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for(int idx=0;idx<_grid->lSites();idx++){
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std::vector<int> lcoor(Nd);
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Tcomplex cc;
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RealD sgn;
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_grid->LocalIndexToLocalCoor(idx,lcoor);
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peekLocalSite(cc,cosha,lcoor);
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assert((double)real(cc)>=1.0);
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assert(fabs((double)imag(cc))<=1.0e-15);
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cc = ScalComplex(::acosh(real(cc)),0.0);
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pokeLocalSite(cc,a,lcoor);
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}
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Wea = ( exp( a) * abs(W) );
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Wema= ( exp(-a) * abs(W) );
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sinha = 0.5*(exp( a) - exp(-a));
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sinhaLs = 0.5*(exp( a*Ls) - exp(-a*Ls));
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coshaLs = 0.5*(exp( a*Ls) + exp(-a*Ls));
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A = one / (abs(W) * sinha * 2.0) * one / (sinhaLs * 2.0);
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F = exp( a*Ls) * (one - Wea + (Wema - one) * mass*mass);
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F = F + exp(-a*Ls) * (Wema - one + (one - Wea) * mass*mass);
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F = F - abs(W) * sinha * 4.0 * mass;
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Bpp = (A/F) * (exp(-a*Ls*2.0) - one) * (one - Wema) * (one - mass*mass * one);
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Bmm = (A/F) * (one - exp(a*Ls*2.0)) * (one - Wea) * (one - mass*mass * one);
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App = (A/F) * (exp(-a*Ls*2.0) - one) * exp(-a) * (exp(-a) - abs(W)) * (one - mass*mass * one);
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Amm = (A/F) * (one - exp(a*Ls*2.0)) * exp(a) * (exp(a) - abs(W)) * (one - mass*mass * one);
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ABpm = (A/F) * abs(W) * sinha * 2.0 * (one + mass * coshaLs * 2.0 + mass*mass * one);
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//P+ source, P- source
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PRsource = (in + g5 * in) * 0.5;
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PLsource = (in - g5 * in) * 0.5;
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//calculate GR, GL
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for(unsigned int ss=1;ss<=Ls;ss++)
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{
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bufR_4d = zero;
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bufL_4d = zero;
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for(unsigned int tt=1;tt<=Ls;tt++)
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{
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//possible sign if W<0
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if((ss+tt)%2==1) signW = abs(W)/W;
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else signW = one;
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unsigned int f = (ss > tt) ? ss-tt : tt-ss; //f = abs(ss-tt)
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//GR
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buf1_4d = zero;
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ExtractSlice(buf1_4d, PRsource, (tt-1), 0);
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//G(s,t)
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bufR_4d = bufR_4d + A * exp(a*Ls) * exp(-a*f) * signW * buf1_4d + A * exp(-a*Ls) * exp(a*f) * signW * buf1_4d;
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//A++*exp(a(s+t))
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bufR_4d = bufR_4d + App * exp(a*ss) * exp(a*tt) * signW * buf1_4d ;
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//A+-*exp(a(s-t))
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bufR_4d = bufR_4d + ABpm * exp(a*ss) * exp(-a*tt) * signW * buf1_4d ;
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//A-+*exp(a(-s+t))
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bufR_4d = bufR_4d + ABpm * exp(-a*ss) * exp(a*tt) * signW * buf1_4d ;
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//A--*exp(a(-s-t))
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bufR_4d = bufR_4d + Amm * exp(-a*ss) * exp(-a*tt) * signW * buf1_4d ;
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//GL
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buf2_4d = zero;
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ExtractSlice(buf2_4d, PLsource, (tt-1), 0);
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//G(s,t)
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bufL_4d = bufL_4d + A * exp(a*Ls) * exp(-a*f) * signW * buf2_4d + A * exp(-a*Ls) * exp(a*f) * signW * buf2_4d;
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//B++*exp(a(s+t))
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bufL_4d = bufL_4d + Bpp * exp(a*ss) * exp(a*tt) * signW * buf2_4d ;
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//B+-*exp(a(s-t))
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bufL_4d = bufL_4d + ABpm * exp(a*ss) * exp(-a*tt) * signW * buf2_4d ;
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//B-+*exp(a(-s+t))
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bufL_4d = bufL_4d + ABpm * exp(-a*ss) * exp(a*tt) * signW * buf2_4d ;
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//B--*exp(a(-s-t))
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bufL_4d = bufL_4d + Bmm * exp(-a*ss) * exp(-a*tt) * signW * buf2_4d ;
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}
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InsertSlice(bufR_4d, GR, (ss-1), 0);
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InsertSlice(bufL_4d, GL, (ss-1), 0);
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}
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//calculate propagator
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for(unsigned int ss=1;ss<=Ls;ss++)
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{
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bufR_4d = zero;
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bufL_4d = zero;
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//(i*gamma_mu*sin(p_mu) - W)*(GL*P- source)
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buf1_4d = zero;
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ExtractSlice(buf1_4d, GL, (ss-1), 0);
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buf2_4d = zero;
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for(int mu=0;mu<Nd;mu++) {
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LatticeCoordinate(kmu,mu);
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RealD TwoPiL = M_PI * 2.0/ latt_size[mu];
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kmu = TwoPiL * kmu + TwoPiL * one * twist[mu];//twisted boundary
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buf2_4d = buf2_4d + sin(kmu)*ci*(Gamma(Gmu[mu])*buf1_4d);
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}
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bufL_4d = buf2_4d - W * buf1_4d;
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//(i*gamma_mu*sin(p_mu) - W)*(GR*P+ source)
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buf1_4d = zero;
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ExtractSlice(buf1_4d, GR, (ss-1), 0);
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buf2_4d = zero;
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for(int mu=0;mu<Nd;mu++) {
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LatticeCoordinate(kmu,mu);
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RealD TwoPiL = M_PI * 2.0/ latt_size[mu];
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kmu = TwoPiL * kmu + TwoPiL * one * twist[mu];//twisted boundary
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buf2_4d = buf2_4d + sin(kmu)*ci*(Gamma(Gmu[mu])*buf1_4d);
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}
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bufR_4d = buf2_4d - W * buf1_4d;
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//(delta(s-1,u) - m*delta(s,1)*delta(u,Ls))*GL
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if(ss==1){
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ExtractSlice(buf1_4d, GL, (Ls-1), 0);
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bufL_4d = bufL_4d - mass*buf1_4d;
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}
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else {
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ExtractSlice(buf1_4d, GL, (ss-2), 0);
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bufL_4d = bufL_4d + buf1_4d;
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}
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//(delta(s+1,u) - m*delta(s,Ls)*delta(u,1))*GR
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if(ss==Ls){
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ExtractSlice(buf1_4d, GR, 0, 0);
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bufR_4d = bufR_4d - mass*buf1_4d;
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}
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else {
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ExtractSlice(buf1_4d, GR, ss, 0);
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bufR_4d = bufR_4d + buf1_4d;
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}
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buf1_4d = bufL_4d + bufR_4d;
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InsertSlice(buf1_4d, out, (ss-1), 0);
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}
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out = out * (-1.0);
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}
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template<class Impl>
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void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const FermionField &in, RealD mass,std::vector<double> twist)
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{
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// what type LatticeComplex
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GridBase *_grid = _FourDimGrid;
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@ -606,6 +821,7 @@ void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const Fe
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RealD TwoPiL = M_PI * 2.0/ latt_size[mu];
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kmu = TwoPiL * kmu;
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kmu = kmu + TwoPiL * one * twist[mu];//momentum for twisted boundary conditions
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sk2 = sk2 + 2.0*sin(kmu*0.5)*sin(kmu*0.5);
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sk = sk + sin(kmu) *sin(kmu);
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@ -619,7 +835,7 @@ void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const Fe
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////////////////////////////////////////////
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// Cosh alpha -> alpha
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////////////////////////////////////////////
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cosha = (one + W*W + sk) / (W*2.0);
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cosha = (one + W*W + sk) / (abs(W)*2.0);
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// FIXME Need a Lattice acosh
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for(int idx=0;idx<_grid->lSites();idx++){
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@ -634,8 +850,8 @@ void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const Fe
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pokeLocalSite(cc,a,lcoor);
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}
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Wea = ( exp( a) * W );
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Wema= ( exp(-a) * W );
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Wea = ( exp( a) * abs(W) );
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Wema= ( exp(-a) * abs(W) );
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num = num + ( one - Wema ) * mass * in;
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denom= ( Wea - one ) + mass*mass * (one - Wema);
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@ -643,7 +859,7 @@ void WilsonFermion5D<Impl>::MomentumSpacePropagatorHt(FermionField &out,const Fe
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}
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template<class Impl>
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void WilsonFermion5D<Impl>::MomentumSpacePropagatorHw(FermionField &out,const FermionField &in,RealD mass)
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void WilsonFermion5D<Impl>::MomentumSpacePropagatorHw(FermionField &out,const FermionField &in,RealD mass,std::vector<double> twist)
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{
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Gamma::Algebra Gmu [] = {
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Gamma::Algebra::GammaX,
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@ -683,6 +899,7 @@ void WilsonFermion5D<Impl>::MomentumSpacePropagatorHw(FermionField &out,const Fe
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RealD TwoPiL = M_PI * 2.0/ latt_size[mu];
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kmu = TwoPiL * kmu;
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kmu = kmu + TwoPiL * one * twist[mu];//momentum for twisted boundary conditions
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sk2 = sk2 + 2.0*sin(kmu*0.5)*sin(kmu*0.5);
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sk = sk + sin(kmu)*sin(kmu);
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