Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States

TL;DR

This paper introduces a fermionic PEPS framework for simulating strongly correlated fermions in two dimensions, enabling efficient ground state approximations and revealing new insights into phase boundaries.

Contribution

The authors develop a straightforward fermionic PEPS method that simplifies implementation and extends tensor network techniques to interacting fermion systems in 2D.

Findings

Lower ground state energies than Hartree-Fock for spinless fermions

Shifted phase boundary between metal and charge-density wave

Comparable energies to Gutzwiller-projected ansatz for t-J model

Abstract

We explain how to implement, in the context of projected entangled-pair states (PEPS), the general procedure of fermionization of a tensor network introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.