Numerical continuum tensor networks in two dimensions

TL;DR

This paper introduces tensor network methods for numerically studying two-dimensional fermionic models in the continuum, demonstrating their effectiveness on free and interacting Fermi gases with large system sizes.

Contribution

It presents novel tensor network approaches tailored for continuum two-dimensional fermionic systems, including multi-grid and isometric coarse-graining techniques.

Findings

Accurate results for free Fermi gas benchmark

Successful simulation of interacting Fermi gas at unitarity

Scalability to large system sizes with up to 1000 sites

Abstract

We describe the use of tensor networks to numerically determine wave functions of interacting two-dimensional fermionic models in the continuum limit. We use two different tensor network states: one based on the numerical continuum limit of fermionic projected entangled pair states obtained via a tensor network formulation of multi-grid, and another based on the combination of the fermionic projected entangled pair state with layers of isometric coarse-graining transformations. We first benchmark our approach on the two-dimensional free Fermi gas then proceed to study the two-dimensional interacting Fermi gas with an attractive interaction in the unitary limit, using tensor networks on grids with up to 1000 sites.