Error with symmetry while measuring the properties of an MPS wavefunction (with conserved QNs)

Question

I was basing on this tutorial:

https://itensor.org/docs.cgi?page=formulas/measure_mps

to implement my own Hamiltonian on a given graph. My code looks as follows:

#include "itensor/all.h"

using namespace itensor;

int
main(int argc, char* argv[])
{
int Nx = 8; // Nx can be understood as the size of an elementary cell
auto N = atoi(argv[1])*Nx;

auto sites = SpinOne(N,{"ConserveQNs=",true});

auto ampo = AutoMPO(sites);

// [Definition of my Hamiltonian]

auto H = toMPO(ampo);

auto state = InitState(sites);

for (int i = 1; i <= N; i++) {
    state.set(i,"Up");
}

auto sweeps = Sweeps(10);
sweeps.maxm() = 50,100,200,300,400;
sweeps.cutoff() = 1E-10;
println(sweeps);

//
// Begin the DMRG calculation
// for the ground state
//
auto [en0,psi0] = dmrg(H,randomMPS(state),sweeps,{"Quiet=",true});

//
// Print the final energies reported by DMRG
//
printfln("\n      Ground State Energy = %.10f",en0);

//
// Measuring Sx, Sy & Sz
//

println("Ground state");
println("\nj | Sx |: ");
for( auto j : range1(N) ) {
    // Re-gauge psi0 to get ready to measure at position j
    psi0.position(j);

    auto ket = psi0(j);
    auto bra = dag(prime(ket,"Site"));

    auto Sxjop = op(sites,"Sx",j);

    //take an inner product
    auto sxj = eltC(bra*Sxjop*ket);
    println(j, " | ", sxj, " | ");
}

return 0;

}

When I run this code I get the following error message:

From line 173, file itdata/qdense.cc
Setting Tensor element non-zero would violate its symmetry.

I know that this problem was mentioned (e.g. here: http://itensor.org/support/1127/error-message-regarding-the-operator-sx2-spintwo-siteset), but the previous posts didn't mention problems while trying to use Sx instead of Sx2.

Moreover, when I modify the following lines:

[...]
auto sites = SpinOne(N,{"ConserveQNs=",true});
[...]
auto [en0,psi0] = dmrg(H,randomMPS(state),sweeps,{"Quiet=",true});
[...]

into:

[...]
auto sites = SpinOne(N,{"ConserveQNs=",false});
[...]
auto [en0,psi0] = dmrg(H,randomMPS(sites),sweeps,{"Quiet=",true});
[...]

everything works fine (but much slower). The change from state to sites in the second line of the example is necessary, or otherwise I get the error:

randomMPS(SiteSet) with QN conservation is ambiguous, use randomMPS(InitState) instead.

Do you have any idea, how to solve this problem?

Answer 1

Hello,

An immediate thing to note is that since the state you are measuring has a well-defined Sz quantum number, measuring Sx will always be zero (since the Sx operator will change the total spin of your state, so Sx|psi> will have a different total Sz from |psi> so <psi|Sx|psi> must be zero).

However, this question brought up the fact that this operation is currently not as easy as it should be to do right now in ITensor. Currently, this is the easiest way I can think of to measure a non-QN conserving operator of a QN-conserving MPS:

auto N = 10;
auto sites = SpinOne(N);

auto state = InitState(sites,"Up");
auto psi = MPS(state);

// Measure Sx on site j
auto j = 3;
psi.position(j);

// Get the site index without QNs
auto sj = removeQNs(sites(j));

// Create a SpinOneSite from the Index
// without QNs to use in the op function
auto Sxj = op(SpinOneSite(sj),"Sx");

auto sxj = elt(psi(j)*Sxj*dag(prime(psi(j),"Site")));

PrintData(sxj);

We are discussing alternative solutions to be able to do this more generally (without manually modifying the Index and then creating the correct Site type), but unfortunately they require fairly technical solutions right now given the current system.

Cheers,
Matt