Universal features of the Abelian Polyakov loop in 1+1 dimension

TL;DR

This paper demonstrates that the Polyakov loop in the 2D lattice Abelian Higgs model exhibits universal finite-size scaling, with tensor renormalization group calculations validated by Monte Carlo simulations, relevant for quantum simulations.

Contribution

It introduces a tensor renormalization group method to compute the Polyakov loop and reveals its universal finite-size scaling behavior in the 2D Abelian Higgs model.

Findings

Polyakov loop energy gap obeys universal finite-size scaling

Tensor renormalization group accurately computes Polyakov loop

Results are relevant for quantum simulation studies

Abstract

We show that the Polyakov loop of the two-dimensional lattice Abelian Higgs model can be calculated using the tensor renormalization group approach. We check the accuracy of the results using standard Monte Carlo simulations. We show that the energy gap produced by the insertion of the Polyakov loop obeys universal finite-size scaling which persists in the time continuum limit. We briefly discuss the relevance of these results for quantum simulations.