Toward tensor renormalization group study of lattice QCD

TL;DR

This paper explores advanced tensor renormalization group techniques tailored for lattice QCD, aiming to overcome computational challenges and improve the analysis of non-Abelian gauge theories.

Contribution

It introduces multi-layer construction and armillary sphere formulation methods to enhance tensor network efficiency in lattice QCD simulations.

Findings

Reduced tensor sizes through new techniques

Elimination of non-local entanglement structures

Potential for improved lattice QCD analysis

Abstract

The tensor renormalization group is a promising complementary approach to traditional Monte Carlo methods for lattice systems, as it is inherently free from the sign problem. We discuss recent developments crucial for its application to lattice QCD: the multi-layer construction for multi-flavor gauge theory and the armillary sphere formulation for non-Abelian gauge theory. These techniques are important for reducing the size of the initial tensor and for eliminating non-local entanglement structures within the tensor network. We present selected numerical results and discuss potential generalizations to lattice QCD.