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210 lines
6.5 KiB
C++
210 lines
6.5 KiB
C++
#ifndef QCD_PSEUDOFERMION_TWO_FLAVOUR_H
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#define QCD_PSEUDOFERMION_TWO_FLAVOUR_H
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namespace Grid{
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namespace QCD{
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// Placeholder comments:
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///////////////////////////////////////
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// Two flavour ratio
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///////////////////////////////////////
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// S = phi^dag V (Mdag M)^-1 V^dag phi
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// dS/du = phi^dag dV (Mdag M)^-1 V^dag phi
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// - phi^dag V (Mdag M)^-1 [ Mdag dM + dMdag M ] (Mdag M)^-1 V^dag phi
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// + phi^dag V (Mdag M)^-1 dV^dag phi
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///////////////////////////////////////
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// One flavour rational
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///////////////////////////////////////
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// S_f = chi^dag * N(M^dag*M)/D(M^dag*M) * chi
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//
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// Here, M is some operator
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// N and D makeup the rat. poly
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//
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// Need
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// dS_f/dU = chi^dag P/Q d[N/D] P/Q chi
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//
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// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
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//
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// N/D is expressed as partial fraction expansion:
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//
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// a0 + \sum_k ak/(M^dagM + bk)
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//
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// d[N/D] is then
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//
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// \sum_k -ak [M^dagM+bk]^{-1} [ dM^dag M + M^dag dM ] [M^dag M + bk]^{-1}
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//
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// Need
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//
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// Mf Phi_k = [MdagM+bk]^{-1} Phi
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// Mf Phi = \sum_k ak [MdagM+bk]^{-1} Phi
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//
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// With these building blocks
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//
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// dS/dU = \sum_k -ak Mf Phi_k^dag [ dM^dag M + M^dag dM ] Mf Phi_k
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// S = innerprodReal(Phi,Mf Phi);
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///////////////////////////////////////
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// One flavour rational ratio
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///////////////////////////////////////
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// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
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//
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// Here, M is some 5D operator and V is the Pauli-Villars field
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// N and D makeup the rat. poly of the M term and P and & makeup the rat.poly of the denom term
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//
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// Need
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// dS_f/dU = chi^dag d[P/Q] N/D P/Q chi
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// + chi^dag P/Q d[N/D] P/Q chi
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// + chi^dag P/Q N/D d[P/Q] chi
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//
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// Here P/Q \sim R_{1/4} ~ (V^dagV)^{1/4}
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// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
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//
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// P/Q is expressed as partial fraction expansion:
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//
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// a0 + \sum_k ak/(V^dagV + bk)
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//
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// d[P/Q] is then
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//
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// \sum_k -ak [V^dagV+bk]^{-1} [ dV^dag V + V^dag dV ] [V^dag V + bk]^{-1}
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//
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// and similar for N/D.
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//
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// Need
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// MpvPhi_k = [Vdag V + bk]^{-1} chi
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//
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// MpvPhi = {a0 + \sum_k ak [Vdag V + bk]^{-1} }chi
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//
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// MfMpvPhi_k = [MdagM+bk]^{-1} MpvPhi
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//
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// MfMpvPhi = {a0 + \sum_k ak [Mdag M + bk]^{-1} } MpvPhi
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//
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// MpvMfMpvPhi_k = [Vdag V + bk]^{-1} MfMpvchi
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//
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// With these building blocks
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//
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// dS/dU =
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// \sum_k -ak MpvPhi_k^dag [ dV^dag V + V^dag dV ] MpvMfMpvPhi_k <- deriv on P left
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// + \sum_k -ak MpvMfMpvPhi_k^\dag [ dV^dag V + V^dag dV ] MpvPhi_k
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// + \sum_k -ak MfMpvPhi_k^dag [ dM^dag M + M^dag dM ] MfMpvPhi_k
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////////////////////////////////////////////////////////////////////////
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// Two flavour pseudofermion action for any dop
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////////////////////////////////////////////////////////////////////////
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template<class GaugeField,class MatrixField,class FermionField>
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class TwoFlavourPseudoFermionAction : public Action<GaugeField> {
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private:
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FermionOperator<FermionField,GaugeField> & FermOp;// the basic operator
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OperatorFunction<FermionField> &DerivativeSolver;
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OperatorFunction<FermionField> &ActionSolver;
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GridBase &Grid;
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FermionField Phi; // the pseudo fermion field for this trajectory
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public:
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/////////////////////////////////////////////////
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// Pass in required objects.
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/////////////////////////////////////////////////
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TwoFlavourPseudoFermionAction(FermionOperator<FermionField,GaugeField> &Op,
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OperatorFunction<FermionField> & DS,
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OperatorFunction<FermionField> & AS,
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GridBase &_Grid
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) : FermOp(Op), DerivativeSolver(DS), ActionSolver(AS), Phi(&_Grid), Grid(_Grid) {
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};
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//////////////////////////////////////////////////////////////////////////////////////
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// Push the gauge field in to the dops. Assume any BC's and smearing already applied
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//////////////////////////////////////////////////////////////////////////////////////
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virtual void init(const GaugeField &U, GridParallelRNG& pRNG) {
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// P(phi) = e^{- phi^dag (MdagM)^-1 phi}
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// Phi = Mdag eta
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// P(eta) = e^{- eta^dag eta}
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//
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// e^{x^2/2 sig^2} => sig^2 = 0.5.
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//
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// So eta should be of width sig = 1/sqrt(2).
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// and must multiply by 0.707....
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//
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// Chroma has this scale factor: two_flavor_monomial_w.h
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// IroIro: does not use this scale. It is absorbed by a change of vars
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// in the Phi integral, and thus is only an irrelevant prefactor for the partition function.
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//
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RealD scale = std::sqrt(0.5);
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FermionField eta(&Grid);
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gaussian(pRNG,eta);
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FermOp.Mdag(eta,Phi);
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Phi=Phi*scale;
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};
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//////////////////////////////////////////////////////
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// S = phi^dag (Mdag M)^-1 phi
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//////////////////////////////////////////////////////
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virtual RealD S(const GaugeField &U) {
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FermOp.ImportGauge(U);
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FermionField X(&Grid);
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FermionField Y(&Grid);
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MdagMLinearOperator<FermionOperator<FermionField,GaugeField> ,FermionField> MdagMOp(FermOp);
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X=zero;
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ActionSolver(MdagMOp,Phi,X);
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MdagMOp.Op(X,Y);
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RealD action = norm2(Y);
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std::cout << GridLogMessage << "Pseudofermion action "<<action<<std::endl;
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return action;
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};
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//////////////////////////////////////////////////////
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// dS/du = - phi^dag (Mdag M)^-1 [ Mdag dM + dMdag M ] (Mdag M)^-1 phi
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// = - phi^dag M^-1 dM (MdagM)^-1 phi - phi^dag (MdagM)^-1 dMdag dM (Mdag)^-1 phi
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//
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// = - Ydag dM X - Xdag dMdag Y
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//
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//////////////////////////////////////////////////////
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virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
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FermOp.ImportGauge(U);
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FermionField X(&Grid);
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FermionField Y(&Grid);
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GaugeField tmp(&Grid);
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MdagMLinearOperator<FermionOperator<FermionField,GaugeField> ,FermionField> MdagMOp(FermOp);
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X=zero;
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DerivativeSolver(MdagMOp,Phi,X);
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MdagMOp.Op(X,Y);
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// Our conventions really make this UdSdU; We do not differentiate wrt Udag here.
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// So must take dSdU - adj(dSdU) and left multiply by mom to get dS/dt.
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FermOp.MDeriv(tmp , Y, X,DaggerNo ); dSdU=tmp;
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FermOp.MDeriv(tmp , X, Y,DaggerYes); dSdU=dSdU+tmp;
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dSdU = Ta(dSdU);
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};
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};
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}
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}
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#endif
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