Improved coarse-graining methods on two dimensional tensor networks including fermions

TL;DR

This paper introduces enhanced coarse-graining algorithms for two-dimensional tensor networks with fermions, improving accuracy in calculating physical quantities in lattice field theories.

Contribution

It develops renormalization group methods with entanglement filtering and loop optimization for tensor networks including Grassmann variables, advancing fermionic lattice simulations.

Findings

Enhanced accuracy in free energy calculations

Better determination of Fisher's zeros

Improved numerical results for fermionic models

Abstract

We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson--Majorana fermions and for the two flavor Gross--Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher's zeros.