QFT Entanglement Entropy, 2D Fermion and Gauge Fields

TL;DR

This paper unifies the calculation of entanglement and Rényi entropies for 2D Dirac fermions on a torus, incorporating various topological effects and resolving issues related to singularities and continuity across sectors.

Contribution

It introduces a comprehensive framework using electromagnetic vertex operators in orbifold CFT to analyze topological phase transitions in entanglement entropy.

Findings

Entanglement entropies are non-singular and continuous across topological sectors.

In infinite space, entropies depend solely on the Wilson loop.

On a circle, entropies reveal subtle dependence on chemical potential at zero temperature.

Abstract

Entanglement and the R\'enyi entropies for Dirac fermions on 2 dimensional torus in the presence of chemical potential, current source, and topological Wilson loop are unified in a single framework by exhausting all the ingredients of the electromagnetic vertex operators of $\mathbb{Z}_n$ orbifold conformal field theory. We employ different normalizations for different topological sectors to organize various topological phase transitions in the context of entanglement entropy. Pictorial representations for the topological transitions are given for the $n=2$ R\'enyi entropy. Our analytic computations reveal numerous novelties and provide resolutions for existing issues. We have settled to provide non-singular entanglement entropies that are also continuous across the topological sectors. Surprisingly, in infinite space, these entropies become exact and depend only on the Wilson loop. On a circle, we resolve to find the entropies subtly depend on the chemical potential at zero temperature, which is useful for probing the ground state energy levels of quantum systems.