Exploring Entanglement Entropy for a Particle on a Torus with constant Metric and constant $U(1)$-Gauge Field

TL;DR

This paper investigates how geometric and topological factors influence entanglement entropy for a particle on a torus with constant metric and gauge field, revealing the importance of metric fixing.

Contribution

It provides new insights into the relationship between geometry, topological terms, and entanglement entropy in quantum systems on a torus.

Findings

Entanglement entropy is non-zero only when the metric is fixed.

Topological $U(1)$-gauge field impacts entanglement properties.

Quantum entanglement plays a key role in quantum dynamics on complex geometries.

Abstract

In this paper, we focus on the entanglement entropy associated with a particle confined to a torus with constant metric and $\theta$-terms related to a constant external $U(1)$-gauge field. Through this investigation, we aim to elucidate the interplay between geometric properties, topological terms, and entanglement entropy. Remarkably, we find that the presence of non-vanishing entanglement entropy is closely tied to fixing the metric. This insight highlights the significant influence of quantum entanglement on our understanding of quantum dynamics in complex spatial configurations.