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Copy pathSC_BathMPO_ImpFirst_TwoChannel_V.h
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SC_BathMPO_ImpFirst_TwoChannel_V.h
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inline void Fill_SCBath_MPO_ImpFirst_TwoChannel_V(MPO& H, const double Eshift, double epsishift1, double epsishift2, double epseff, 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 ( {"Sz", 0},{"Nf", 0} ),
cupC ( {"Sz", +1},{"Nf",+1} ),
cdnC ( {"Sz", -1},{"Nf",+1} ),
cupA ( {"Sz", -1},{"Nf",-1} ),
cdnA ( {"Sz", +1},{"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, 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)) * epseff; // due to V the impurity level energy also shifts!
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("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);
W += p.sites.op("Ntot",i) * setElt(right(9)) * p.V1imp;
W += p.sites.op("Ntot",i) * setElt(right(10)) * p.V2imp;
}
// sites 2 ... N-1 are matrices
for(auto i : range1(2,((length(H)+1)/2)-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] + epsishift1 + p.sc1->Ec()*(1.0-2.0*p.sc1->n0())); // !
W += p.sites.op("Nup",i) * setElt(left(1),right(2)) * p.sc1->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn",i) * setElt(left(1),right(2)) * (-1.) * p.sc1->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Nupdn",i) * setElt(left(1),right(2)) * (p.sc1->g() * pow(p.sc1->y(i-1), 2) + 2.0*p.sc1->Ec()); // !
W += p.sites.op("Cdn*Cup",i) * setElt(left(1),right(7)) * p.sc1->g() * p.sc1->y(i-1);
W += p.sites.op("Cdagup*Cdagdn",i) * setElt(left(1),right(8)) * p.sc1->g() * p.sc1->y(i-1);
W += p.sites.op("Ntot", i) * setElt(left(1),right(9)) * 2.0*p.sc1->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("Id",i)*setElt(left(10),right(10));
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.sc1->y(i-1);
W += p.sites.op("Cdn*Cup",i) *setElt(left(8),right(2)) * p.sc1->y(i-1);
W += p.sites.op("Ntot",i) *setElt(left(9),right(2)); // !
}
// central matrix is the same as the ones for SC1, just connecting terms are zero to break up the SCs
{
int i = ((length(H)+1)/2);
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] + epsishift1 + p.sc1->Ec()*(1.0-2.0*p.sc1->n0())); // !
W += p.sites.op("Nup",i) * setElt(left(1),right(2)) * p.sc1->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn",i) * setElt(left(1),right(2)) * (-1.) * p.sc1->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Nupdn",i) * setElt(left(1),right(2)) * (p.sc1->g() * pow(p.sc1->y(i-1), 2) + 2.0*p.sc1->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("Id",i)*setElt(left(10),right(10));
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.sc1->y(i-1);
W += p.sites.op("Cdn*Cup",i) *setElt(left(8),right(2)) * p.sc1->y(i-1);
W += p.sites.op("Ntot",i) *setElt(left(9),right(2)); // !
}
// onwards the same, just for sc2
int shift = (length(H)-1)/2; // number of matrices for one channel. i-shift is the index of the i-th level in the second channel.
for(auto i : range1( ((length(H)+1)/2)+1, 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] + epsishift2 + p.sc2->Ec()*(1.0-2.0*p.sc2->n0())); // !
W += p.sites.op("Nup",i) * setElt(left(1),right(2)) * p.sc2->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn",i) * setElt(left(1),right(2)) * (-1.) * p.sc2->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Nupdn",i) * setElt(left(1),right(2)) * (p.sc2->g() * (p.sc2->y(i-1-shift), 2) + 2.0*p.sc2->Ec()); // !
W += p.sites.op("Cdn*Cup",i) * setElt(left(1),right(7)) * p.sc2->g() * p.sc2->y(i-1-shift);
W += p.sites.op("Cdagup*Cdagdn",i) * setElt(left(1),right(8)) * p.sc2->g() * p.sc2->y(i-1-shift);
W += p.sites.op("Ntot", i) * setElt(left(1),right(10)) * 2.0*p.sc2->Ec(); // 10 here also!
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(10),right(10)); // 10 here, to accumulate the sum of nSC2
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.sc2->y(i-1-shift);
W += p.sites.op("Cdn*Cup",i) *setElt(left(8),right(2)) * p.sc2->y(i-1-shift);
W += p.sites.op("Ntot",i) *setElt(left(10),right(2)); // this is dimension 10, as the sum_i n_i has to be transferred all the way to the imp site, in order to multiply it by nimp!
}
//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] + epsishift2 + p.sc2->Ec()*(1.0-2.0*p.sc2->n0())); // !
W += p.sites.op("Nup", i) * setElt(left(1)) * p.sc2->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Ndn", i) * setElt(left(1)) * (-1) * p.sc2->EZ()/2.0; // bulk Zeeman energy
W += p.sites.op("Nupdn",i) * setElt(left(1)) * (p.sc2->g() * pow(p.sc2->y(i-1-shift), 2) + 2.0*p.sc2->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.sc2->y(i-1-shift);
W += p.sites.op("Cdn*Cup", i) * setElt(left(8)) * p.sc2->y(i-1-shift);
W += p.sites.op("Ntot", i) * setElt(left(10)); // this is dimension 10, as it has to be transferred all the way to the imp site, in order to multiply it by nimp!
}
}