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Elemental force term for Wilson dslash added and tests thereof passing.

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Now need to construct pseudofermion two flavour, ratio, one flavour, ratio
action fragments.
This commit is contained in:
Peter Boyle
2015-07-26 10:54:38 +09:00
parent 1d70a45d84
commit d9d4c5916a
18 changed files with 758 additions and 42 deletions
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88
lib/qcd/action/fermion/WilsonFermion.h
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@ -24,11 +24,95 @@ namespace Grid {
// half checkerboard operaions
void Meooe (const LatticeFermion &in, LatticeFermion &out);
void MeooeDag (const LatticeFermion &in, LatticeFermion &out);
virtual void Mooee (const LatticeFermion &in, LatticeFermion &out); // remain virtual so we
virtual void MooeeDag (const LatticeFermion &in, LatticeFermion &out); // can derive Clover
virtual void MooeeInv (const LatticeFermion &in, LatticeFermion &out); // from Wilson base
virtual void MooeeInvDag (const LatticeFermion &in, LatticeFermion &out);
////////////////////////
//
// Force term: d/dtau S = 0
//
// It is simplest to consider the two flavour force term
//
// S[U,phi] = phidag (MdagM)^-1 phi
//
// But simplify even this to
//
// S[U,phi] = phidag MdagM phi
//
// (other options exist depending on nature of action fragment.)
//
// Require momentum be traceless anti-hermitian to move within group manifold [ P = i P^a T^a ]
//
// Define the HMC hamiltonian
//
// H = 1/2 Tr P^2 + S(U,phi)
//
// .
// U = P U (lorentz & color indices multiplied)
//
// Hence
//
// .c c c c
// U = U P = - U P (c == dagger)
//
// So, taking some liberty with implicit indices
// . . .c c
// dH/dt = 0 = Tr P P +Tr[ U dS/dU + U dS/dU ]
//
// . c c
// = Tr P P + i Tr[ P U dS/dU - U P dS/dU ]
//
// . c c
// = Tr P (P + i ( U dS/dU - P dS/dU U ]
//
// . c c
// => P = -i [ U dS/dU - dS/dU U ] generates HMC EoM
//
// Simple case work this out using S = phi^dag MdagM phi for wilson:
// c c
// dSdt = dU_xdt dSdUx + dUxdt dSdUx
//
// = Tr i P U_x [ (\phi^\dag)_x (1+g) (M \phi)_x+\mu +(\phi^\dag M^\dag)_x (1-g) \phi_{x+\mu} ]
// c
// - i U_x P [ (\phi^\dag)_x+mu (1-g) (M \phi)_x +(\phi^\dag M^\dag)_(x+\mu) (1+g) \phi_{x} ]
//
// = i [(\phi^\dag)_x ]_j P_jk [U_x(1+g) (M \phi)_x+\mu]_k (1)
// + i [(\phi^\dagM^\dag)_x]_j P_jk [U_x(1-g) (\phi)_x+\mu]_k (2)
// - i [(\phi^\dag)_x+mu (1-g) U^dag_x]_j P_jk [(M \phi)_xk (3)
// - i [(\phi^\dagM^\dag)_x+mu (1+g) U^dag_x]_j P_jk [ \phi]_xk (4)
//
// Observe that (1)* = (4)
// (2)* = (3)
//
// Write as .
// 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 )
//
// where (x) denotes outer product in colour and spins are traced.
//
// Need only evaluate (1) and (2) [Chroma] or (2) and (4) [IroIro] and take the
// traceless anti hermitian part (of term in brackets w/o the "i")
//
// Generalisation to S=phi^dag (MdagM)^{-1} phi is simple:
//
// For more complicated DWF etc... apply product rule in differentiation
//
////////////////////////
void DhopDeriv (LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
void DhopDerivEO(LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
void DhopDerivOE(LatticeGaugeField &mat,const LatticeFermion &U,const LatticeFermion &V,int dag);
// Extra support internal
void DerivInternal(CartesianStencil & st,
LatticeDoubledGaugeField & U,
LatticeGaugeField &mat,
const LatticeFermion &A,
const LatticeFermion &B,
int dag);
// non-hermitian hopping term; half cb or both
void Dhop (const LatticeFermion &in, LatticeFermion &out,int dag);
void DhopOE(const LatticeFermion &in, LatticeFermion &out,int dag);
@ -37,6 +121,7 @@ namespace Grid {
// Multigrid assistance
void Mdir (const LatticeFermion &in, LatticeFermion &out,int dir,int disp);
void DhopDir(const LatticeFermion &in, LatticeFermion &out,int dir,int disp);
void DhopDirDisp(const LatticeFermion &in, LatticeFermion &out,int dirdisp,int gamma,int dag);
///////////////////////////////////////////////////////////////
// Extra methods added by derived
@ -59,7 +144,8 @@ namespace Grid {
static int HandOptDslash; // these are a temporary hack
static int MortonOrder;
protected:
// protected:
public:
RealD mass;