Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density

TL;DR

This paper employs tensor renormalization group techniques to study the (1+1)-dimensional SU(2) principal chiral model at finite density, demonstrating effective discretization and capturing key phenomena like the Silver-Blaze effect.

Contribution

It introduces a tensor renormalization group approach combined with Gauss-Legendre quadrature for discretizing SU(2), enabling analysis at finite density.

Findings

Consistent internal energy with strong and weak coupling predictions at zero chemical potential.

Successful discretization of SU(2) Lie group using Gauss-Legendre quadrature.

Observation of the Silver-Blaze phenomenon in the number density at finite chemical potential.

Abstract

We apply the tensor renormalization group method to the (1+1)-dimensional SU(2) principal chiral model at finite chemical potential with the use of the Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal energy at vanishing chemical potential $\mu=0$ shows good consistency with the prediction of the strong and weak coupling expansions. This indicates an effectiveness of the Gauss-Legendre quadrature for the partitioning of the SU(2) Lie group. In the finite density region with $\mu\ne 0$ at the strong coupling we observe the Silver-Blaze phenomenon for the number density.