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Entanglement entropy and Wilson loop. (English) Zbl 1441.81150

Summary: We study both entanglement and the Rényi 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. Topological transitions for the generalized 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 generalized Rényi 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.

MSC:

81V74 Fermionic systems in quantum theory
81P40 Quantum coherence, entanglement, quantum correlations
81P17 Quantum entropies
57R18 Topology and geometry of orbifolds
81V10 Electromagnetic interaction; quantum electrodynamics
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