int main(void){
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_init();
#endif
CheMPS2::Initialize::Init();
//Square 2D Hubbard model with PBC
const int L_linear = 3; // Linear size
const int L_square = L_linear * L_linear; // Number of orbitals
const int group = 0; // C1 symmetry
const double U = 5.0; // On-site repulsion
const double T = -1.0; // Hopping term
const int N = 9; // Number of electrons
const int TwoS = 1; // Two times the spin
const int Irrep = 0; // Irrep = A (C1 symmetry)
//Create the Hamiltonian (eightfold permutation symmetry is OK for site basis)
int * irreps = new int[L_square];
for (int cnt=0; cnt<L_square; cnt++){ irreps[cnt] = 0; }
//The Hamiltonian initializes all its matrix elements to 0.0
CheMPS2::Hamiltonian * Ham = new CheMPS2::Hamiltonian(L_square, group, irreps);
delete [] irreps;
//Fill with the site-basis matrix elements
for (int cnt=0; cnt<L_square; cnt++){ Ham->setVmat(cnt,cnt,cnt,cnt,U); }
for (int ix=0; ix<L_linear; ix++){
for (int iy=0; iy<L_linear; iy++){
const int idx1 = ix + L_linear * iy; // This site
const int idx2 = (( ix + 1 ) % L_linear) + L_linear * iy; // Right neighbour (PBC)
const int idx3 = ix + L_linear * ((( iy + 1 ) % L_linear)); //Upper neighbour (PBC)
Ham->setTmat(idx1,idx2,T);
Ham->setTmat(idx1,idx3,T);
}
}
//The problem object
CheMPS2::Problem * Prob = new CheMPS2::Problem(Ham, TwoS, N, Irrep);
//The convergence scheme
CheMPS2::ConvergenceScheme * OptScheme = new CheMPS2::ConvergenceScheme(2);
//OptScheme->setInstruction(instruction, DSU(2), Econvergence, maxSweeps, noisePrefactor);
OptScheme->setInstruction(0, 500, 1e-10, 3, 0.05);
OptScheme->setInstruction(1, 1000, 1e-10, 10, 0.0 );
//Run ground state calculation
CheMPS2::DMRG * theDMRG = new CheMPS2::DMRG(Prob, OptScheme);
const double EnergySite = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
//Clean up DMRG
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
//Hack: overwrite the matrix elements in momentum space (4-fold symmetry!!!) directly in the Problem object
theDMRG = new CheMPS2::DMRG(Prob, OptScheme); // Prob->construct_mxelem() is called now
for (int orb1=0; orb1<L_square; orb1++){
const int k1x = orb1 % L_linear;
const int k1y = orb1 / L_linear;
const double Telem1 = 2*T*( cos((2*M_PI*k1x)/L_linear)
+ cos((2*M_PI*k1y)/L_linear) );
for (int orb2=0; orb2<L_square; orb2++){
const int k2x = orb2 % L_linear;
const int k2y = orb2 / L_linear;
const double Telem2 = 2*T*( cos((2*M_PI*k2x)/L_linear)
+ cos((2*M_PI*k2y)/L_linear) );
for (int orb3=0; orb3<L_square; orb3++){
const int k3x = orb3 % L_linear;
const int k3y = orb3 / L_linear;
for (int orb4=0; orb4<L_square; orb4++){
const int k4x = orb4 % L_linear;
const int k4y = orb4 / L_linear;
const bool kx_conservation = (((k1x+k2x) % L_linear) == ((k3x+k4x) % L_linear))?true:false;
const bool ky_conservation = (((k1y+k2y) % L_linear) == ((k3y+k4y) % L_linear))?true:false;
double temp = 0.0;
if ( kx_conservation && ky_conservation ){ temp += U/L_square; }
if (( orb1 == orb3 ) && ( orb2 == orb4 )){ temp += (Telem1+Telem2)/(N-1); }
Prob->setMxElement(orb1,orb2,orb3,orb4,temp);
}
}
}
}
theDMRG->PreSolve(); // New matrix elements require reconstruction of complementary renormalized operators
const double EnergyMomentum = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
//Clean up
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
delete OptScheme;
delete Prob;
delete Ham;
//Check succes
const bool success = ( fabs( EnergySite - EnergyMomentum ) < 1e-8 ) ? true : false;
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_finalize();
#endif
cout << "================> Did test 10 succeed : ";
if (success){
cout << "yes" << endl;
return 0; //Success
}
cout << "no" << endl;
return 7; //Fail
}
int main(void){
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_init();
#endif
CheMPS2::Initialize::Init();
//The Hamiltonian: 1D Hubbard model
const int L = 10;
const int Group = 0;
const double U = 2.0;
const double T = -1.0;
int * irreps = new int[L];
for (int cnt=0; cnt<L; cnt++){ irreps[cnt] = 0; }
//The Hamiltonian initializes all its matrix elements to 0.0
CheMPS2::Hamiltonian * Ham = new CheMPS2::Hamiltonian(L, Group, irreps);
delete [] irreps;
for (int cnt=0; cnt<L; cnt++){ Ham->setVmat(cnt,cnt,cnt,cnt,U); }
for (int cnt=0; cnt<L-1; cnt++){ Ham->setTmat(cnt,cnt+1,T); }
//The targeted state
const int TwoS = 5;
const int N = 9;
const int Irrep = 0;
CheMPS2::Problem * Prob = new CheMPS2::Problem(Ham, TwoS, N, Irrep);
//The convergence scheme
CheMPS2::ConvergenceScheme * OptScheme = new CheMPS2::ConvergenceScheme(2);
//OptScheme->setInstruction(instruction, DSU(2), Econvergence, maxSweeps, noisePrefactor);
OptScheme->setInstruction(0, 30, 1e-10, 3, 0.1);
OptScheme->setInstruction(1, 1000, 1e-10, 10, 0.0);
//Run ground state calculation
CheMPS2::DMRG * theDMRG = new CheMPS2::DMRG(Prob, OptScheme);
const double EnergyDMRG = theDMRG->Solve();
theDMRG->calc2DMandCorrelations();
#ifdef CHEMPS2_MPI_COMPILATION
if ( CheMPS2::MPIchemps2::mpi_rank() == MPI_CHEMPS2_MASTER )
#endif
{
theDMRG->getCorrelations()->Print();
}
//Clean up DMRG
if (CheMPS2::DMRG_storeMpsOnDisk){ theDMRG->deleteStoredMPS(); }
if (CheMPS2::DMRG_storeRenormOptrOnDisk){ theDMRG->deleteStoredOperators(); }
delete theDMRG;
delete OptScheme;
delete Prob;
//Calculate FCI reference energy
double EnergyFCI = 0.0;
#ifdef CHEMPS2_MPI_COMPILATION
if ( CheMPS2::MPIchemps2::mpi_rank() == MPI_CHEMPS2_MASTER )
#endif
{
const int Nel_up = ( N + TwoS ) / 2;
const int Nel_down = ( N - TwoS ) / 2;
const double maxMemWorkMB = 10.0;
const int FCIverbose = 1;
CheMPS2::FCI * theFCI = new CheMPS2::FCI(Ham, Nel_up, Nel_down, Irrep, maxMemWorkMB, FCIverbose);
EnergyFCI = theFCI->GSDavidson(NULL);
delete theFCI;
}
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::broadcast_array_double( &EnergyFCI, 1, MPI_CHEMPS2_MASTER );
#endif
//Clean up the Hamiltonian
delete Ham;
//Check succes
const bool success = ( fabs( EnergyDMRG - EnergyFCI ) < 1e-8 ) ? true : false;
#ifdef CHEMPS2_MPI_COMPILATION
CheMPS2::MPIchemps2::mpi_finalize();
#endif
cout << "================> Did test 4 succeed : ";
if (success){
cout << "yes" << endl;
return 0; //Success
}
cout << "no" << endl;
return 7; //Fail
}