# Tensor renormalization group study of the non-Abelian Higgs model in two dimensions

## TL;DR

This paper applies the tensor renormalization group method to the two-dimensional SU(2) gauge-Higgs model, demonstrating its effectiveness and superior performance over Monte Carlo simulations in calculating the Polyakov loop correlation function.

## Contribution

The paper introduces a tensor formulation of the 2D SU(2) gauge-Higgs model and validates TRG against Monte Carlo, highlighting its advantages for specific observables.

## Key findings

- Excellent agreement between TRG and Monte Carlo for expectation values.
- TRG outperforms Monte Carlo in computing the Polyakov loop correlation function.
- TRG provides a more efficient approach for static quark potential calculations.

## Abstract

We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In practice we find the TRG method to be far superior to Monte Carlo simulation for calculations of the Polyakov loop correlation function which is used to extract the static quark potential.