Overlap between two MPS after time evolution

Question

Hi all,

fist of all, I am using the version 1.2.

I am trying to compute the following quantity:

G{ij}(t)= < 0 | e^{iHt} * ai * e^{-iHt} * a^{\dagger}_j | 0 >

where | 0 > is the ground state of the Kitaev chain with Hamiltonian H, and a and a^{\dagger} are the usual fermionic operator. My idea is to compute the two time evolution of the two states separately:

• a^{\dagger}_j | 0 >
• |0>

in order to obtain:

• e^{-iHt} * a^{\dagger}_j | 0 >
• e^{-iHt} | 0 >.

Then I apply the operator a^{\dagger}i on the second state in order to obtain the state a{\dagger}i * e^{-iHt} | 0 >. Finally, I would like to take the bra - ket product between this two states for computing the previous quantity G_ij(t).

I attach the code:

 auto sites = Spinless(N,{"ConserveNf",false});
 auto ampo = AutoMPO(sites);

for(int i=1; i<N; ++i) {
   ampo += -1.0*w, "Cdag",   i,  "C", i+1;
   ampo += -1.0*w, "Cdag", i+1,  "C", i;

   ampo += +1.0*delta,               "C",   i,   "C", i+1;
   ampo += +1.0*std::conj(delta), "Cdag", i+1,"Cdag", i;

   ampo += +1.0*Uint, "Nint", i,  "Nint", i+1;
}

for(int i = 1; i <= N; ++i) {
   ampo += -1.0*mu, "N", i;
}

auto H = IQMPO(ampo);
auto state = InitState(sites);

auto psi = IQMPS(state);

auto energy = dmrg(psi,H,sweeps,{"Quiet",true});

// Print the final energy reported by DMRG
printfln("\nGround State Energy = %.10f \n\n", energy);


// Time Evolution
auto tau = 0.01;
auto expH = toExpH<IQTensor>(ampo,tau*Cplx_i);

auto args = Args("Cutoff=",1E-9,"Maxm=",3000);
auto ttotal = 3.0;
auto nt = int(ttotal/tau+(1e-9*(ttotal/tau)));

for(int n = 1; n <= nt; ++n) {

   for(int i = 1; i <=N; ++i) {   
      for(int j = i; j <=N; ++j) {

         if (j > i) {           

            auto op_i = sites.op("Cdag",   i);              
            auto op_j = sites.op("Cdag",   j);

            // Creating the new MPS for the ket 
            auto psi_ket = psi;
            psi_ket.position(j);                
            auto new_psi_ket = op_j*psi_ket.A(j);
            new_psi_ket.noprime();
            psi_ket.setA(j, new_psi_ket);


            // Evolving the ket
            psi_ket = exactApplyMPO<IQTensor>(expH,psi_ket,args);
            normalize(psi_ket);

            // Evolving the state for the bra
            psi = exactApplyMPO<IQTensor>(expH,psi,args);
            normalize(psi);

            // Replace the operator CDag in the state for the bra
            psi.position(i);                
            auto new_psi = op_i*psi_ket.A(i);
            new_psi.noprime();
            psi.setA(i, new_psi);


            psi.position(1); 
            psi_ket.position(1);

            auto result = overlapC(psi, psi_ket);
            Print(result);




         } 

      }
   }

   printfln("MPO: Time %d, Maximum MPS bond dimension after time evolution is %d", n*tau,maxM(psi));

}

The problem is that I obtain the following error:

From line 211, file /Users/giuseppe/Desktop/iTensor/ITensor/itensor/itensor_interface.ih

Wrong number of IndexVals passed to real/cplx (expected 2, got 0)

Wrong number of IndexVals passed to real/cplx (expected 2, got 0)

Any idea?

Thank you very much.

Comments

Hi, this error usually occurs when the contraction of two ITensors is supposed to result in a scalar but instead the tensor still has one or more indices. Do you know at which line of your code this error is occurring?  - Miles

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Hi Miles,

the error occurs in the overlapC function. Without that line everything seems fine.

Thank you.

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Thanks, I see. Did you print out the MPS psi and psi_ket to inspect whether they have compatible indices and a correct MPS structure (neighboring tensors share indices)? That’s the most likely issue because otherwise overlapC should always succeed.

Best, Miles

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Thanks, now it works. Actually, it was a problem with neighboring indices. Thank you very much!

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Great! Glad you got it sorted out

Answer 1

(Please see above discussion.)