# Fermionic multi-scale entanglement renormalization ansatz

## TL;DR

This paper develops a fermionic version of the multi-scale entanglement renormalization ansatz (MERA), enabling efficient simulation of fermionic lattice systems in two dimensions, with benchmark results confirming its validity.

## Contribution

It introduces a detailed fermionic MERA formalism and algorithm, extending previous bosonic MERA to fermionic systems for the first time.

## Key findings

- Benchmark results for free fermions on large lattices
- Validation of the fermionic MERA approach
- Applicability to generic tensor network algorithms

## Abstract

In a recent contribution [arXiv:0904:4151] entanglement renormalization was generalized to fermionic lattice systems in two spatial dimensions. Entanglement renormalization is a real-space coarse-graining transformation for lattice systems that produces a variational ansatz, the multi-scale entanglement renormalization ansatz (MERA), for the ground states of local Hamiltonians. In this paper we describe in detail the fermionic version of the MERA formalism and algorithm. Starting from the bosonic MERA, which can be regarded both as a quantum circuit or in relation to a coarse-graining transformation, we indicate how the scheme needs to be modified to simulate fermions. To confirm the validity of the approach, we present benchmark results for free and interacting fermions on a square lattice with sizes between $6 \times 6$ and $162\times 162$ and with periodic boundary conditions. The present formulation of the approach applies to generic tensor network algorithms.