Entanglement entropy and Wilson loop

TL;DR

This paper investigates entanglement and R'enyi entropies in 2D massless Dirac fermions with topological Wilson loops, revealing topological transitions and providing exact entropy formulas independent of chemical potential and current source.

Contribution

It introduces a novel analysis of entanglement entropies in the presence of topological Wilson loops, connecting electric and magnetic operators in orbifold theories and deriving exact entropy results.

Findings

Exact entanglement and R'enyi entropy formulas depending only on Wilson loops.

Topological transitions driven by electric and magnetic parameters.

Continuity of entropies across different topological sectors.

Abstract

We study both entanglement and the R\'enyi entropies for the 2 dimensional massless Dirac fermions in the presence of topological Wilson loops, which are qualitatively different from those with a chemical potential and a current source. In the language of $\mathbb{Z}_n$ orbifold theories, the Wilson loop is interpreted as an electric operator while the orbifold twist operator as a magnetic operator. Generalized topological transitions for the entropies are driven by both electric and magnetic parameters via the restriction on the operator's conformal weight. By adapting different normalizations for different topological sectors, we achieve two goals: entanglement entropy can be obtained with a smooth limit from the R\'enyi entropy, and the entropies are continuous across the different topological sectors that include general Wilson loops winding sectors. We provide exact results for the entropies in infinite space, which depend only on the topological Wilson loops, independent of the chemical potential and the current source.