Fermionic Projected Entangled Pair States

TL;DR

This paper introduces fermionic PEPS (fPEPS), a new class of tensor network states for simulating fermionic lattice systems, extending existing methods for spin systems to fermions and providing exact ground state representations.

Contribution

It extends PEPS to fermionic systems, establishes a mapping between the two, and demonstrates fPEPS as exact ground states of certain fermionic Hamiltonians.

Findings

fPEPS can describe fermionic lattice systems in arbitrary dimensions

A mapping between PEPS and fPEPS enables extension of simulation methods

fPEPS can be exact ground states of critical fermionic Hamiltonians

Abstract

We introduce a family of states, the fPEPS, which describes fermionic systems on lattices in arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the PEPS, which efficiently approximate ground and thermal states of spin systems with short-range interactions. We give an explicit mapping between those families, which allows us to extend previous simulation methods to fermionic systems. We also show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians. We give an example of such a Hamiltonian, exhibiting criticality while obeying an area law.