Tensor-network simulation of the strong-coupling $U(N)$ model

TL;DR

This paper uses tensor network methods to analyze the strong-coupling $U(N)$ model, revealing insights into chiral symmetry breaking and confirming results with Monte Carlo simulations in higher dimensions.

Contribution

It introduces tensor network techniques to study the $U(N)$ model in the strong-coupling regime, providing new computational insights into chiral symmetry breaking.

Findings

Chiral condensate behavior matches Monte Carlo results.

Chiral symmetry is spontaneously broken in the infinite volume and zero mass limit.

Tensor networks effectively study higher-dimensional lattice models.

Abstract

We apply tensor network methods to study the strong-coupling $U(N)$ model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and find good agreement with Monte Carlo simulations. Particularly interesting is the study of chiral symmetry breaking as a function of the mass and the volume, which clearly shows that this symmetry is spontaneously broken in the limit of infinite volume and zero mass.