A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories

TL;DR

This paper introduces a novel tensor network approach to efficiently incorporate multiple fermion flavors in lattice gauge theories, enabling detailed studies of phase transitions and phenomena like the Silver Blaze effect.

Contribution

It presents a new method that separates site tensors by flavor and introduces gauge fields as replicas, improving computational efficiency in tensor renormalization group calculations.

Findings

Successfully applied to 2D Abelian gauge theories with up to 4 flavors

Demonstrated effectiveness in studying chiral phase transition

Enabled analysis of Silver Blaze phenomenon

Abstract

We propose a new technique to incorporate multiple fermion flavors in the tensor renormalization group method for lattice gauge theories, where fermions are treated by the Grassmann tensor network formalism. The basic idea is to separate the site tensor into multiple layers associated with each flavor and to introduce the gauge field in each layer as replicas, which are all identified later. This formulation, after introducing an appropriate compression scheme in the network, enables us to reduce the size of the initial tensor with high efficiency compared with a naive implementation. The usefulness of this formulation is demonstrated by investigating the chiral phase transition and the Silver Blaze phenomenon in 2D Abelian gauge theories with $N_{\rm f}$ flavors of Wilson fermions up to $N_{\rm f}=4$.