FermionSiteSU2xSU2.h

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#ifndef FERMIONSITESU2xSU2_H_
#define FERMIONSITESU2xSU2_H_
 
#include "symmetry/kind_dummies.h"
 
#include "DmrgTypedefs.h"
 
#include "symmetry/S1xS2.h"
#include "symmetry/SU2.h"
 
#include "tensors/SiteOperatorQ.h"
 
template <typename Symmetry> class FermionSite;
 
template <>
class FermionSite<Sym::S1xS2<Sym::SU2<Sym::SpinSU2>,Sym::SU2<Sym::ChargeSU2> > >
{
    typedef double Scalar;
    typedef Sym::S1xS2<Sym::SU2<Sym::SpinSU2>,Sym::SU2<Sym::ChargeSU2> > Symmetry;
    typedef SiteOperatorQ<Symmetry,Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> > OperatorType;
public:
    FermionSite() {};
    FermionSite (bool REMOVE_DOUBLE, bool REMOVE_EMPTY, bool REMOVE_UP, bool REMOVE_DN, int mfactor_input=1, int k_input=0);
    
    OperatorType Id_1s() const {return Id_1s_;}
    OperatorType F_1s() const {return F_1s_;}
    
    OperatorType c_1s(SUB_LATTICE G) const { if(G == A) {return cA_1s_;} return cB_1s_; }
    OperatorType cdag_1s(SUB_LATTICE G) const {return c_1s(G).adjoint();}
 
    OperatorType ns_1s() const {return Id_1s()-nh_1s();}
    OperatorType nh_1s() const {return nh_1s_;}
 
    OperatorType S_1s() const {return S_1s_;}
    
    OperatorType T_1s() const {return T_1s_;}
 
    Qbasis<Symmetry> basis_1s() const {return basis_1s_;}
protected:
    Qbasis<Symmetry> basis_1s_;
 
    OperatorType Id_1s_; //identity
    OperatorType F_1s_; //Fermionic sign
 
    OperatorType cA_1s_; //annihilation
    OperatorType cB_1s_; //annihilation
 
    OperatorType nh_1s_; //holon number
    OperatorType S_1s_; //orbital spin
    OperatorType T_1s_; //orbital isospin
};
 
FermionSite<Sym::S1xS2<Sym::SU2<Sym::SpinSU2>,Sym::SU2<Sym::ChargeSU2> > >::
FermionSite (bool REMOVE_DOUBLE, bool REMOVE_EMPTY, bool REMOVE_UP, bool REMOVE_DN, int mfactor_input, int k_input)
{
    bool REMOVE_SPINON = (REMOVE_UP or REMOVE_DN)?        true:false;
    bool REMOVE_HOLON  = (REMOVE_DOUBLE or REMOVE_EMPTY)? true:false;
    
    //create basis for one Fermionic Site
    typename Symmetry::qType Q; //empty occupied state
    Eigen::Index inner_dim;
    std::vector<std::string> ident;
    //assert(!U_IS_INFINITE and "For charge SU2, U is not allowed to be infinity. This breaks the Charge-SU2 Symmetry.");
    
    if (!REMOVE_HOLON)
    {
        Q = {1,2};
        inner_dim = 1;
        ident.push_back("holon");
        basis_1s_.push_back(Q,inner_dim,ident);
        ident.clear();
    }
    if (!REMOVE_SPINON)
    {
        Q={2,1}; //spinon state
        inner_dim = 1;
        ident.push_back("spinon");
        basis_1s_.push_back(Q,inner_dim,ident);
        ident.clear();
    }
    
    Id_1s_ = OperatorType({1,1},basis_1s_,"id");
    F_1s_ = OperatorType({1,1},basis_1s_,"F");
    cA_1s_ = OperatorType({2,2},basis_1s_,"c(A)");
    cB_1s_ = OperatorType({2,2},basis_1s_,"c(B)");
    nh_1s_ = OperatorType({1,1},basis_1s_,"nh");
    T_1s_ = OperatorType({1,3},basis_1s_,"T");
    S_1s_ = OperatorType({3,1},basis_1s_,"S");
    
    // create operators one orbitals
    if (!REMOVE_HOLON)  Id_1s_("holon", "holon") = 1.;
    if (!REMOVE_SPINON) Id_1s_("spinon", "spinon") = 1.;
    
    if (!REMOVE_HOLON)  F_1s_("holon", "holon") = 1.;
    if (!REMOVE_SPINON) F_1s_("spinon", "spinon") = -1.;
    
    if (!REMOVE_HOLON)  nh_1s_("holon","holon") = 1.;
    
    if (!REMOVE_HOLON)  T_1s_( "holon", "holon" ) = std::sqrt(0.75);
    
    if (!REMOVE_SPINON) S_1s_( "spinon", "spinon" ) = std::sqrt(0.75);
    
    if (!REMOVE_HOLON and !REMOVE_SPINON) cA_1s_( "spinon", "holon" ) = std::sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_SPINON) cA_1s_( "holon", "spinon" ) = std::sqrt(2.);
    
    if (!REMOVE_HOLON and !REMOVE_SPINON) cB_1s_( "spinon", "holon" ) = std::sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_SPINON) cB_1s_( "holon", "spinon" ) = -1.*std::sqrt(2.);
}
 
#endif //FERMIONSITESU2xSU2_H_