Tensor renormalization group study of the two-dimensional lattice U(1) gauge-Higgs model with a topological $\theta$ term under L\"uscher's admissibility condition

TL;DR

This paper applies tensor renormalization group methods to study a 2D lattice U(1) gauge-Higgs model with a topological term, overcoming simulation challenges posed by complex action and topological freezing.

Contribution

It demonstrates how L"uscher's admissibility condition can be effectively integrated with tensor renormalization group techniques to handle topological terms in lattice gauge theories.

Findings

Successfully resolves complex action problem.

Addresses topological freezing issue.

Shows the advantage of admissibility condition in discretized topological terms.

Abstract

We investigate the two-dimensional lattice U(1) gauge-Higgs model with a topological term, employing L\"uscher's admissibility condition. The standard Monte Carlo simulation for this model is hindered not only by the complex action problem due to the topological term but also by the topological freezing problem originating from the admissibility condition. Resolving both obstacles simultaneously with the tensor renormalization group approach, we show the advantage of the admissibility condition in dealing with the topological term discretized with the so-called field-theoretical definition.