# Higher order tensor renormalization group for relativistic fermion systems

## TL;DR

This paper introduces a Grassmann higher order tensor renormalization group method for simulating relativistic fermion systems on lattices, demonstrating its effectiveness through comparisons with exact and existing methods.

## Contribution

The paper develops a novel Grassmann higher order tensor renormalization group algorithm for fermionic systems, enabling efficient coarse-graining of tensor networks with Grassmann variables.

## Key findings

- The new method accurately reproduces known results for relativistic fermion systems.
- It extends tensor network techniques to include Grassmann variables.
- Validation against exact and previous methods confirms its reliability.

## Abstract

We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods.