Fermionic Implementation of Projected Entangled Pair States Algorithm

TL;DR

This paper introduces an efficient variational algorithm for simulating two-dimensional fermionic quantum systems using fermionic projected entangled pair states, eliminating the need for string-bond contraction and demonstrating good accuracy on lattice models.

Contribution

The paper presents a novel fermionic PEPS algorithm that simplifies tensor network contraction, improving efficiency for 2D fermionic systems.

Findings

Accurate results on a 10x10 fermionic lattice model.

Qualitative success on interacting fermionic systems.

No need for string-bond in tensor network contraction.

Abstract

We present and implement an efficient variational method to simulate two-dimensional finite size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there is no need for an extra string-bond for contracting the tensor network. The method is tested on a bi-linear fermionic model on a square lattice for sizes up to ten by ten where good relative accuracy is achieved. Qualitatively good results are also obtained for an interacting fermionic system.