$SU(2)$ principal chiral model with tensor renormalization group on a cubic lattice

TL;DR

This paper applies tensor renormalization group methods to the 3D $SU(2)$ principal chiral model, analyzing phase transitions and thermodynamics, and aligns well with Monte Carlo results, advancing towards finite-density QCD studies.

Contribution

It demonstrates the effectiveness of tensor renormalization group methods in studying phase transitions in the 3D $SU(2)$ model, connecting to finite-density QCD research.

Findings

Results agree with Monte Carlo estimates

Consistent with renormalization group scaling

Progress towards finite-density QCD studies

Abstract

We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean $SU(2)$ principal chiral field model with the triad tensor renormalization group (tTRG) and the anisotropic tensor renormalization group (ATRG) methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density QCD in four dimensions using tensor network methods.