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Copy pathSC_BathMPO_Ec_SO.h
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SC_BathMPO_Ec_SO.h
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inline void Fill_SCBath_MPO_Ec_SO(MPO& H, const double Eshift, const std::vector<double>& eps_,
const std::vector<double>& v_, const params &p)
{
//QN objects are necessary to have abelian symmetries in MPS
QN qn0 ( {"Nf", 0} ),
cupC ( {"Nf",+1} ),
cdnC ( {"Nf",+1} ),
cupA ( {"Nf",-1} ),
cdnA ( {"Nf",-1} ),
cSoC ( {"Nf",+1} ),
cSoA ( {"Nf",-1} );
std::vector<Index> links;
links.push_back( Index() );
//first we create the link indices which carry quantum number information
for(auto i : range1(length(H))){
links.push_back(Index( qn0, 2,
cupC, 1,
cdnC, 1,
cupA, 1,
cdnA, 1,
cupC+cdnC, 1,
cupA+cdnA, 1,
qn0, 1,
cSoC, 2,
cSoA, 2,
Out, "Link" ));
}
//then we just fill the MPO tensors which can be viewed
//as matrices (vectors) of operators. if one multiplies
//all matrices togehter one obtains the hamiltonian.
//therefore the tensor on the first and last site must be column/ row vectors
//and all sites between matrices
//first site is a vector:
{
int i = 1;
ITensor& W = H.ref(i);
Index right = links.at(i);
W = ITensor(right, p.sites.si(i), p.sites.siP(i) );
W += p.sites.op("Id",i) * setElt(right(1));
W += p.sites.op("Ntot",i) * setElt(right(2)) * p.qd->eps(); // not eps_[i-1]!
W += p.sites.op("Nup",i) * setElt(right(2)) * p.qd->EZ()/2.0; // impurity Zeeman energy
W += p.sites.op("Ndn",i) * setElt(right(2)) * (-1) * p.qd->EZ()/2.0; // impurity Zeeman energy
W += p.sites.op("S+", i) * setElt(right(2)) * p.qd->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("S-", i) * setElt(right(2)) * p.qd->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("Nupdn",i) * setElt(right(2)) * p.qd->U(); // not Ueff!
W += p.sites.op("Id",i) * setElt(right(2)) * Eshift;
W += p.sites.op("Cup*F",i) * setElt(right(3)) * (-1);
W += p.sites.op("Cdn*F",i) * setElt(right(4)) * (-1);
W += p.sites.op("Cdagup*F",i) * setElt(right(5)) * (+1);
W += p.sites.op("Cdagdn*F",i) * setElt(right(6)) * (+1);
}
// sites 2 ... N-1 are matrices
for(auto i : range1(2,length(H)-1)){
ITensor& W = H.ref(i);
Index left = dag( links.at(i-1) );
Index right = links.at(i);
W = ITensor(left, right, p.sites.si(i), p.sites.siP(i) );
W += p.sites.op("Id",i) * setElt(left(1), right(1));
W += p.sites.op("Ntot",i) * setElt(left(1),right(2)) * (eps_[i-1] + p.sc->Ec()*(1.0-2.0*p.sc->n0())); // !
W += p.sites.op("Nup",i) * setElt(left(1),right(2)) * p.sc->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn",i) * setElt(left(1),right(2)) * (-1.) * p.sc->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("S+", i) * setElt(left(1),right(2)) * p.sc->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("S-", i) * setElt(left(1),right(2)) * p.sc->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("Nupdn",i) * setElt(left(1),right(2)) * (p.sc->g() * pow(p.sc->y(i-1), 2) + 2.0*p.sc->Ec()); // !
W += p.sites.op("Cdn*Cup",i) * setElt(left(1),right(7)) * p.sc->g() * p.sc->y(i-1);
W += p.sites.op("Cdagup*Cdagdn",i) * setElt(left(1),right(8)) * p.sc->g() * p.sc->y(i-1);
W += p.sites.op("Ntot", i) * setElt(left(1),right(9)) * 2.0*p.sc->Ec(); // !
W += p.sites.op("Id",i) * setElt(left(2),right(2));
W += p.sites.op("F" ,i) * setElt(left(3),right(3));
W += p.sites.op("F" ,i) * setElt(left(4),right(4));
W += p.sites.op("F" ,i) * setElt(left(5),right(5));
W += p.sites.op("F" ,i) * setElt(left(6),right(6));
W += p.sites.op("Id",i) * setElt(left(7),right(7));
W += p.sites.op("Id",i) * setElt(left(8),right(8));
W += p.sites.op("Id",i) * setElt(left(9),right(9));
W += p.sites.op("Cdagup",i) * setElt(left(3),right(2))* v_[i-1];
W += p.sites.op("Cdagdn",i) * setElt(left(4),right(2))* v_[i-1];
W += p.sites.op("Cup", i) * setElt(left(5),right(2))* v_[i-1];
W += p.sites.op("Cdn", i) * setElt(left(6),right(2))* v_[i-1];
W += p.sites.op("Cdagup*Cdagdn",i) * setElt(left(7),right(2)) * p.sc->y(i-1);
W += p.sites.op("Cdn*Cup",i) * setElt(left(8),right(2)) * p.sc->y(i-1);
W += p.sites.op("Ntot",i) * setElt(left(9),right(2));
//The spin orbit coupling part
W += p.sites.op("Cdagup",i) * setElt(left(10),right(2)) * Complex_i * p.sc->l();
W += p.sites.op("Cdagdn",i) * setElt(left(11),right(2)) * Complex_i * p.sc->l();
W += p.sites.op("Cup",i) * setElt(left(12),right(2)) * Complex_i * p.sc->l();
W += p.sites.op("Cdn",i) * setElt(left(13),right(2)) * Complex_i * p.sc->l();
W += p.sites.op("Cdn*F",i) * setElt(left(1),right(10));// * (-1.);
W += p.sites.op("Cup*F",i) * setElt(left(1),right(11));// * (-1.);
W += p.sites.op("Cdagdn*F",i) * setElt(left(1),right(12));
W += p.sites.op("Cdagup*F",i) * setElt(left(1),right(13));
W += p.sites.op("F",i) * setElt(left(10),right(10));
W += p.sites.op("F",i) * setElt(left(11),right(11));
W += p.sites.op("F",i) * setElt(left(12),right(12));
W += p.sites.op("F",i) * setElt(left(13),right(13));
}
//site N is a vector again
{
int i = length(H);
ITensor& W = H.ref(i);
Index left = dag( links.at(i-1) );
W = ITensor(left, p.sites.si(i), p.sites.siP(i) );
W += p.sites.op("Ntot", i) * setElt(left(1)) * (eps_[i-1] + p.sc->Ec()*(1.0-2.0*p.sc->n0())); // !
W += p.sites.op("Nup", i) * setElt(left(1)) * p.sc->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn", i) * setElt(left(1)) * (-1) * p.sc->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("S+", i) * setElt(left(1)) * p.sc->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("S-", i) * setElt(left(1)) * p.sc->EZx()/2.0; // magnetic field in the x direction
W += p.sites.op("Nupdn",i) * setElt(left(1)) * (p.sc->g() * pow(p.sc->y(i-1), 2) + 2.0*p.sc->Ec()); // !
W += p.sites.op("Id", i) * setElt(left(2)) ;
W += p.sites.op("Cdagup",i) * setElt(left(3)) * v_[i-1];
W += p.sites.op("Cdagdn",i) * setElt(left(4)) * v_[i-1];
W += p.sites.op("Cup", i) * setElt(left(5)) * v_[i-1];
W += p.sites.op("Cdn", i) * setElt(left(6)) * v_[i-1];
W += p.sites.op("Cdagup*Cdagdn",i) * setElt(left(7)) * p.sc->y(i-1);
W += p.sites.op("Cdn*Cup", i) * setElt(left(8)) * p.sc->y(i-1);
W += p.sites.op("Ntot", i) * setElt(left(9));
//The spin orbit coupling part
W += p.sites.op("Cdagup", i) * setElt(left(10)) * Complex_i * p.sc->l();
W += p.sites.op("Cdagdn", i) * setElt(left(11)) * Complex_i * p.sc->l();
W += p.sites.op("Cup", i) * setElt(left(12)) * Complex_i * p.sc->l();
W += p.sites.op("Cdn", i) * setElt(left(13)) * Complex_i * p.sc->l();
}
}