Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians

TL;DR

This paper advances the simulation of two-dimensional fermionic lattice models with Projected Entangled-Pair States by incorporating next-nearest neighbor interactions, providing benchmark results and improved accuracy for gapped phases.

Contribution

It introduces a method to include next-nearest neighbor terms in fermionic PEPS algorithms and benchmarks these models against analytical and Monte Carlo results.

Findings

More accurate results for gapped phases than gapless ones.

Successful incorporation of next-nearest neighbor interactions in fermionic PEPS.

Benchmark comparisons validate the method against established results.

Abstract

In a recent contribution [Phys. Rev. B 81, 165104 (2010)] fermionic Projected Entangled-Pair States (PEPS) were used to approximate the ground state of free and interacting spinless fermion models, as well as the $t$-$J$ model. This paper revisits these three models in the presence of an additional next-nearest hopping amplitude in the Hamiltonian. First we explain how to account for next-nearest neighbor Hamiltonian terms in the context of fermionic PEPS algorithms based on simulating time evolution. Then we present benchmark calculations for the three models of fermions, and compare our results against analytical, mean-field, and variational Monte Carlo results, respectively. Consistent with previous computations restricted to nearest-neighbor Hamiltonians, we systematically obtain more accurate (or better converged) results for gapped phases than for gapless ones.