FermionSiteU1xSU2.h

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#ifndef FERMIONSITEU1xSU2_H_
#define FERMIONSITEU1xSU2_H_
 
#include "symmetry/kind_dummies.h"
 
#include "DmrgTypedefs.h"
 
#include "symmetry/S1xS2.h"
#include "symmetry/SU2.h"
#include "symmetry/U1.h"
 
#include "tensors/SiteOperatorQ.h"
 
template <typename Symmetry> class FermionSite;
 
template <>
class FermionSite<Sym::S1xS2<Sym::U1<Sym::SpinU1>, Sym::SU2<Sym::ChargeSU2> > >
{
    typedef double Scalar;
    typedef Sym::S1xS2<Sym::U1<Sym::SpinU1>, Sym::SU2<Sym::ChargeSU2> > Symmetry;
    typedef SiteOperatorQ<Symmetry,Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> > OperatorType;
    typedef SiteOperatorQ<Symmetry,Eigen::Matrix<complex<Scalar>,Eigen::Dynamic,Eigen::Dynamic> > ComplexOperatorType;
    
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(SPIN_INDEX sigma, SUB_LATTICE G) const
    {
        if      (sigma == UP and G == A) {return cupA_1s_;}
        else if (sigma == UP and G == B) {return cupB_1s_;}
        else if (sigma == DN and G == A) {return cdnA_1s_;}
        return cdnB_1s_; //else: sigma==DN and G==B
    }
    OperatorType cdag_1s(SPIN_INDEX sigma, SUB_LATTICE G) const {return c_1s(sigma,G).adjoint();}
    
    OperatorType n_1s() const {return n_1s(UP) + n_1s(DN);}
    OperatorType n_1s(SPIN_INDEX sigma) const { if (sigma == UP) {return nup_1s_;} return ndn_1s_; }
    OperatorType ns_1s() const {return Id_1s()-nh_1s();}
    OperatorType nh_1s() const {return nh_1s_;}
    
    OperatorType Sz_1s() const {return Sz_1s_;}
    OperatorType Sp_1s() const {return Sp_1s_;}
    OperatorType Sm_1s() const {return Sm_1s_;}
    ComplexOperatorType exp_ipiSz_1s() const {return exp_ipiSz_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 cupA_1s_; //annihilation
    OperatorType cdnA_1s_; //annihilation
    OperatorType cupB_1s_; //annihilation
    OperatorType cdnB_1s_; //annihilation
    
    OperatorType nup_1s_; //particle number
    OperatorType ndn_1s_; //particle number
    OperatorType nh_1s_; //holon number
    OperatorType Sz_1s_; //orbital spin
    OperatorType Sp_1s_; //orbital spin
    OperatorType Sm_1s_; //orbital spin
    OperatorType T_1s_; //orbital isospin
    ComplexOperatorType exp_ipiSz_1s_; //string order term
};
 
FermionSite<Sym::S1xS2<Sym::U1<Sym::SpinU1>, 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_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 = {0,2};
        inner_dim = 1;
        ident.push_back("holon");
        basis_1s_.push_back(Q,inner_dim,ident);
        ident.clear();
    }
    if (!REMOVE_UP)
    {
        Q={+1,1}; //singly occupied state up
        inner_dim = 1;
        ident.push_back("up");
        basis_1s_.push_back(Q,inner_dim,ident);
        ident.clear();
    }
    if (!REMOVE_DN)
    {
        Q={-1,1}; //singly occupied state down
        inner_dim = 1;
        ident.push_back("dn");
        basis_1s_.push_back(Q,inner_dim,ident);
        ident.clear();
    }
    
    Id_1s_ = OperatorType({0,1},basis_1s_,"id");
    F_1s_ = OperatorType({0,1},basis_1s_,"F");
    cupA_1s_ = OperatorType({-1,2},basis_1s_,"c↑(A)");
    cupB_1s_ = OperatorType({-1,2},basis_1s_,"c↑(B)");
    cdnA_1s_ = OperatorType({+1,2},basis_1s_,"c↓(A)");
    cdnB_1s_ = OperatorType({+1,2},basis_1s_,"c↓(B)");
    nh_1s_ = OperatorType({0,1},basis_1s_,"nh");
    T_1s_ = OperatorType({0,3},basis_1s_,"T");
    exp_ipiSz_1s_ = ComplexOperatorType({0,1},basis_1s_,"exp_ipiSz");
    
    // create operators one orbitals
    if (!REMOVE_HOLON) Id_1s_("holon", "holon") = 1.;
    if (!REMOVE_UP)    Id_1s_("up", "up") = 1.;
    if (!REMOVE_DN)    Id_1s_("dn", "dn") = 1.;
    
    if (!REMOVE_HOLON) F_1s_("holon", "holon") = 1.;
    if (!REMOVE_UP)    F_1s_("up", "up") = -1.;
    if (!REMOVE_DN)    F_1s_("dn", "dn") = -1.;
    
    if (!REMOVE_HOLON) nh_1s_("holon","holon") = 1.;
    
    if (!REMOVE_HOLON) T_1s_( "holon","holon") = std::sqrt(0.75);
    
    if (!REMOVE_HOLON and !REMOVE_DN) cupA_1s_( "dn", "holon" ) = sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_UP) cupA_1s_( "holon", "up" ) = -1.;
    
    if (!REMOVE_HOLON and !REMOVE_UP) cdnA_1s_( "up", "holon" ) = sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_DN) cdnA_1s_( "holon", "dn" ) = 1.;
    
    if (!REMOVE_HOLON and !REMOVE_DN) cupB_1s_( "dn", "holon" ) = -1.*sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_UP) cupB_1s_( "holon", "up" ) = -1.;
    
    if (!REMOVE_HOLON and !REMOVE_UP) cdnB_1s_( "up", "holon" ) = -1.*sqrt(2.);
    if (!REMOVE_HOLON and !REMOVE_DN) cdnB_1s_( "holon", "dn" ) = 1.;
    
    nup_1s_ = std::sqrt(0.5) * OperatorType::prod(cupA_1s_.adjoint(),cupA_1s_,{0,1});
    ndn_1s_ = std::sqrt(0.5) * OperatorType::prod(cdnA_1s_.adjoint(),cdnA_1s_,{0,1});
    
    Sz_1s_ = 0.5 * (std::sqrt(0.5) * OperatorType::prod(cupA_1s_.adjoint(),cupA_1s_,{0,1}) - std::sqrt(0.5) * OperatorType::prod(cdnA_1s_.adjoint(),cdnA_1s_,{0,1}));
    Sp_1s_ = -std::sqrt(0.5) * OperatorType::prod(cupA_1s_.adjoint(),cdnA_1s_,{+2,1});
    Sm_1s_ = -std::sqrt(0.5) * OperatorType::prod(cdnA_1s_.adjoint(),cupA_1s_,{-2,1});
    //Sm_1s_ = Sp_1s_.adjoint();
    
    if (!REMOVE_UP) exp_ipiSz_1s_("up","up") = +1.i;
    if (!REMOVE_DN) exp_ipiSz_1s_("dn","dn") = -1.i;
    if (!REMOVE_HOLON) exp_ipiSz_1s_("holon","holon") = 1.;
}
 
#endif //FERMIONSITESU2xU1_H_