Periodic boundary conditions for spinless fermions

DMRG and Numerical Methods
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1

I am attaching the screenshot of my code for spinless interacting fermion with NN hopping and NN interaction with periodic boundary condition. I have calculated the ground state energy ftom DMRG. The valve of ground state energy is not matching with the ground state energy calculated from Exact diagonalization. If i remove PBC ground state energy is matching with ED. Please have a look of this picture of my code and let me know if i have incorporated the PBC correctly or not.

Thanks

Screenshot from 2022-10-02 15-47-59

2

It look ok, but a few possible things (in order of more likely to less likely):

  • PBC is much more challenging than OBC for DMRG. How many sweeps did you do?
  • your initial state is a very difficult one for DMRG to converge because the particles start out all next to each other. It would be better to put them on every other site, say.
  • lastly, there may be a subtle issue with the sign of the periodic hopping term, especially if you have an odd number of particles, which may also be an issue with your ED code possibly. It can be subtle to do PBC correctly for fermions. So just try both signs of the periodic hopping in both codes.

Mainly I would just try other cases (does U=0 work?) and try harder to converge the DMRG.

Lastly, why are you using PBC? There can be good reasons to, but generally it scales much worse for DMRG and OBC is often the better choice.

For more information on this:
<https://itensor.github.io/ITensors.jl/stable/faq/DMRG.html#What-boundary-conditions-should-I-choose:-open,-periodic,-or-infinite?>

(Link above not working properly but the PBC part is at the end of that page.)