void CheMPS2::DMRG::calc2DM(){
//First get the whole MPS into left-canonical form
int index = Prob->gL()-2;
Sobject * denS = new Sobject(index,denBK->gIrrep(index),denBK->gIrrep(index+1),denBK);
denS->Join(MPS[index],MPS[index+1]);
Heff Solver(denBK, Prob);
double Energy = 0.0;
double ** VeffTilde = NULL;
if (Exc_activated){
VeffTilde = new double*[nStates-1];
for (int cnt=0; cnt<nStates-1; cnt++){
VeffTilde[cnt] = new double[denS->gKappa2index(denS->gNKappa())];
calcVeffTilde(VeffTilde[cnt], denS, cnt);
}
}
Energy = Solver.SolveDAVIDSON(denS, Ltensors, Atensors, Btensors, Ctensors, Dtensors, S0tensors, S1tensors, F0tensors, F1tensors, Qtensors, Xtensors, nStates-1, VeffTilde);
if (Exc_activated){
for (int cnt=0; cnt<nStates-1; cnt++){ delete [] VeffTilde[cnt]; }
delete [] VeffTilde;
}
Energy += Prob->gEconst();
if (Energy<MinEnergy){ MinEnergy = Energy; }
denS->Split(MPS[index],MPS[index+1],OptScheme->getD(OptScheme->getNInstructions()-1),true,true);
delete denS;
cout << "*********************" << endl;
cout << "** 2DM calculation **" << endl;
cout << "*********************" << endl;
updateMovingRightSafe(index);
TensorDiag * Norm = new TensorDiag(Prob->gL(), denBK);
MPS[Prob->gL()-1]->QR(Norm);
delete Norm;
//Then calculate step by step the 2DM
if (!the2DMallocated){
the2DMallocated = true;
the2DM = new TwoDM(denBK, Prob);
}
for (int siteindex=Prob->gL()-1; siteindex>=0; siteindex--){
the2DM->FillSite(MPS[siteindex], Ltensors, F0tensors, F1tensors, S0tensors, S1tensors);
if (siteindex>0){
TensorDiag * Left = new TensorDiag(siteindex, denBK);
MPS[siteindex]->LQ(Left);
MPS[siteindex-1]->RightMultiply(Left);
delete Left;
updateMovingLeftSafe2DM(siteindex-1);
}
}
//Then perform two checks: double trace & energy
double NtimesNminus1 = the2DM->doubletrace2DMA();
cout << " N(N-1) = " << denBK->gN() * (denBK->gN() - 1) << " and calculated by double trace of the 2DM-A = " << NtimesNminus1 << endl;
double Energy2DMA = the2DM->calcEnergy();
cout << " Energy obtained by Heffective at edge = " << Energy << " and as Econst + 0.5*trace(2DM-A*Ham) = " << Energy2DMA << endl;
}
void CheMPS2::DMRG::calcVeffTilde(double * result, Sobject * currentS, int state_number){
int dimTot = currentS->gKappa2index(currentS->gNKappa());
for (int cnt=0; cnt<dimTot; cnt++){ result[cnt] = 0.0; }
int index = currentS->gIndex();
const int dimL = std::max(denBK->gMaxDimAtBound(index), Exc_BKs[state_number]->gMaxDimAtBound(index) );
const int dimR = std::max(denBK->gMaxDimAtBound(index+2), Exc_BKs[state_number]->gMaxDimAtBound(index+2) );
double * workmem = new double[dimL * dimR];
//Construct Sup
Sobject * Sup = new Sobject(index,Exc_BKs[state_number]->gIrrep(index),Exc_BKs[state_number]->gIrrep(index+1),Exc_BKs[state_number]);
Sup->Join(Exc_MPSs[state_number][index],Exc_MPSs[state_number][index+1]);
//Construct VeffTilde
const double prefactor = sqrt(Exc_Eshifts[state_number]) / (Prob->gTwoS() + 1.0);
for (int ikappa=0; ikappa<currentS->gNKappa(); ikappa++){
int NL = currentS->gNL(ikappa);
int TwoSL = currentS->gTwoSL(ikappa);
int IL = currentS->gIL(ikappa);
int N1 = currentS->gN1(ikappa);
int N2 = currentS->gN2(ikappa);
int TwoJ = currentS->gTwoJ(ikappa);
int NR = currentS->gNR(ikappa);
int TwoSR = currentS->gTwoSR(ikappa);
int IR = currentS->gIR(ikappa);
//Check if block also exists for other MPS
int kappaSup = Sup->gKappa(NL, TwoSL, IL, N1, N2, TwoJ, NR, TwoSR, IR);
if (kappaSup!=-1){
int dimLdown = denBK->gCurrentDim(index, NL,TwoSL,IL);
int dimLup = Exc_BKs[state_number]->gCurrentDim(index, NL,TwoSL,IL);
int dimRdown = denBK->gCurrentDim(index+2,NR,TwoSR,IR);
int dimRup = Exc_BKs[state_number]->gCurrentDim(index+2,NR,TwoSR,IR);
//Do sqrt( (TwoJR+1) * Eshift ) / (TwoStarget+1) times (OL * Sup)_{block} --> workmem
double * SupPart = Sup->gStorage() + Sup->gKappa2index(kappaSup);
double alpha = prefactor * sqrt(TwoSR+1.0);
if (index==0){
int dimBlock = dimLup * dimRup;
int inc = 1;
dcopy_(&dimBlock,SupPart,&inc,workmem,&inc);
dscal_(&dimBlock,&alpha,workmem,&inc);
} else {
char notrans = 'N';
double beta = 0.0;
double * Opart = Exc_Overlaps[state_number][index-1]->gStorage(NL,TwoSL,IL,NL,TwoSL,IL);
dgemm_(¬rans,¬rans,&dimLdown,&dimRup,&dimLup,&alpha,Opart,&dimLdown,SupPart,&dimLup,&beta,workmem,&dimLdown);
}
//Do (workmem * OR)_{block} --> result + jumpCurrentS
int jumpCurrentS = currentS->gKappa2index(ikappa);
if (index==Prob->gL()-2){
int dimBlock = dimLdown * dimRdown;
int inc = 1;
dcopy_(&dimBlock, workmem, &inc, result + jumpCurrentS, &inc);
} else {
char trans = 'T';
char notrans = 'N';
alpha = 1.0;
double beta = 0.0; //set
double * Opart = Exc_Overlaps[state_number][index+1]->gStorage(NR,TwoSR,IR,NR,TwoSR,IR);
dgemm_(¬rans,&trans,&dimLdown,&dimRdown,&dimRup,&alpha,workmem,&dimLdown,Opart,&dimRdown,&beta,result+jumpCurrentS,&dimLdown);
}
}
}
//Deallocate everything
delete Sup;
delete [] workmem;
}