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179 lines
6.9 KiB
C++
179 lines
6.9 KiB
C++
#ifndef GRID_QCD_WILSON_FERMION_H
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#define GRID_QCD_WILSON_FERMION_H
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namespace Grid {
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namespace QCD {
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class WilsonFermion : public FermionOperator<LatticeFermion,LatticeGaugeField>
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{
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public:
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///////////////////////////////////////////////////////////////
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// Implement the abstract base
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///////////////////////////////////////////////////////////////
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GridBase *GaugeGrid(void) { return _grid ;}
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GridBase *GaugeRedBlackGrid(void) { return _cbgrid ;}
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GridBase *FermionGrid(void) { return _grid;}
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GridBase *FermionRedBlackGrid(void) { return _cbgrid;}
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// override multiply
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virtual RealD M (const LatticeFermion &in, LatticeFermion &out);
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virtual RealD Mdag (const LatticeFermion &in, LatticeFermion &out);
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// half checkerboard operaions
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void Meooe (const LatticeFermion &in, LatticeFermion &out);
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void MeooeDag (const LatticeFermion &in, LatticeFermion &out);
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virtual void Mooee (const LatticeFermion &in, LatticeFermion &out); // remain virtual so we
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virtual void MooeeDag (const LatticeFermion &in, LatticeFermion &out); // can derive Clover
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virtual void MooeeInv (const LatticeFermion &in, LatticeFermion &out); // from Wilson base
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virtual void MooeeInvDag (const LatticeFermion &in, LatticeFermion &out);
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////////////////////////
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//
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// Force term: d/dtau S = 0
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//
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// It is simplest to consider the two flavour force term
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//
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// S[U,phi] = phidag (MdagM)^-1 phi
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//
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// But simplify even this to
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//
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// S[U,phi] = phidag MdagM phi
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//
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// (other options exist depending on nature of action fragment.)
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//
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// Require momentum be traceless anti-hermitian to move within group manifold [ P = i P^a T^a ]
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//
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// Define the HMC hamiltonian
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//
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// H = 1/2 Tr P^2 + S(U,phi)
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//
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// .
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// U = P U (lorentz & color indices multiplied)
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//
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// Hence
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//
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// .c c c c
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// U = U P = - U P (c == dagger)
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//
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// So, taking some liberty with implicit indices
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// . . .c c
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// dH/dt = 0 = Tr P P +Tr[ U dS/dU + U dS/dU ]
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//
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// . c c
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// = Tr P P + i Tr[ P U dS/dU - U P dS/dU ]
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//
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// . c c
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// = Tr P (P + i ( U dS/dU - P dS/dU U ]
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//
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// . c c
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// => P = -i [ U dS/dU - dS/dU U ] generates HMC EoM
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//
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// Simple case work this out using S = phi^dag MdagM phi for wilson:
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// c c
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// dSdt = dU_xdt dSdUx + dUxdt dSdUx
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//
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// = Tr i P U_x [ (\phi^\dag)_x (1+g) (M \phi)_x+\mu +(\phi^\dag M^\dag)_x (1-g) \phi_{x+\mu} ]
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// c
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// - i U_x P [ (\phi^\dag)_x+mu (1-g) (M \phi)_x +(\phi^\dag M^\dag)_(x+\mu) (1+g) \phi_{x} ]
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//
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// = i [(\phi^\dag)_x ]_j P_jk [U_x(1+g) (M \phi)_x+\mu]_k (1)
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// + i [(\phi^\dagM^\dag)_x]_j P_jk [U_x(1-g) (\phi)_x+\mu]_k (2)
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// - i [(\phi^\dag)_x+mu (1-g) U^dag_x]_j P_jk [(M \phi)_xk (3)
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// - i [(\phi^\dagM^\dag)_x+mu (1+g) U^dag_x]_j P_jk [ \phi]_xk (4)
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//
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// Observe that (1)* = (4)
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// (2)* = (3)
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//
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// Write as .
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// P_{kj} = - i ( [U_x(1+g) (M \phi)_x+\mu] (x) [(\phi^\dag)_x] + [U_x(1-g) (\phi)_x+\mu] (x) [(\phi^\dagM^\dag)_x] - h.c )
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//
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// where (x) denotes outer product in colour and spins are traced.
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//
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// Need only evaluate (1) and (2) [Chroma] or (2) and (4) [IroIro] and take the
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// traceless anti hermitian part (of term in brackets w/o the "i")
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//
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// Generalisation to S=phi^dag (MdagM)^{-1} phi is simple:
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//
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// For more complicated DWF etc... apply product rule in differentiation
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//
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////////////////////////
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void DhopDeriv (LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
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void DhopDerivEO(LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
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void DhopDerivOE(LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
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// Extra support internal
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void DerivInternal(CartesianStencil & st,
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LatticeDoubledGaugeField & U,
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LatticeGaugeField &mat,
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const LatticeFermion &A,
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const LatticeFermion &B,
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int dag);
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// non-hermitian hopping term; half cb or both
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void Dhop (const LatticeFermion &in, LatticeFermion &out,int dag);
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void DhopOE(const LatticeFermion &in, LatticeFermion &out,int dag);
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void DhopEO(const LatticeFermion &in, LatticeFermion &out,int dag);
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// Multigrid assistance
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void Mdir (const LatticeFermion &in, LatticeFermion &out,int dir,int disp);
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void DhopDir(const LatticeFermion &in, LatticeFermion &out,int dir,int disp);
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void DhopDirDisp(const LatticeFermion &in, LatticeFermion &out,int dirdisp,int gamma,int dag);
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///////////////////////////////////////////////////////////////
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// Extra methods added by derived
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///////////////////////////////////////////////////////////////
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void DhopInternal(CartesianStencil & st,
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LatticeDoubledGaugeField &U,
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const LatticeFermion &in,
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LatticeFermion &out,
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int dag);
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// Constructor
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WilsonFermion(LatticeGaugeField &_Umu,GridCartesian &Fgrid,GridRedBlackCartesian &Hgrid,RealD _mass);
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// DoubleStore
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virtual void ImportGauge(const LatticeGaugeField &_Umu);
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void DoubleStore(LatticeDoubledGaugeField &Uds,const LatticeGaugeField &Umu);
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///////////////////////////////////////////////////////////////
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// Data members require to support the functionality
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///////////////////////////////////////////////////////////////
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static int HandOptDslash; // these are a temporary hack
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static int MortonOrder;
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// protected:
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public:
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RealD mass;
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GridBase * _grid;
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GridBase * _cbgrid;
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static const int npoint=8;
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static const std::vector<int> directions ;
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static const std::vector<int> displacements;
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//Defines the stencils for even and odd
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CartesianStencil Stencil;
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CartesianStencil StencilEven;
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CartesianStencil StencilOdd;
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// Copy of the gauge field , with even and odd subsets
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LatticeDoubledGaugeField Umu;
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LatticeDoubledGaugeField UmuEven;
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LatticeDoubledGaugeField UmuOdd;
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// Comms buffer
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std::vector<vHalfSpinColourVector,alignedAllocator<vHalfSpinColourVector> > comm_buf;
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};
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}
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}
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#endif
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