Notes on Entanglement in Abelian Gauge Theories

Abstract

We streamline and generalize the recent progress in understanding entanglement between spatial regions in Abelian gauge theories. We provide an unambiguous and explicit prescription for calculating entanglement entropy in a ${\mathbb{Z}}_N$ lattice gauge theory. The main idea is that the lattice should be split into two disjoint regions of links separated by a buffer zone of plaquettes. We show that the previous calculations of the entanglement entropy can be realized as special cases of our setup, and we argue that the ambiguities reported in the previous work can be understood as basis choices for gauge-invariant operators living in the buffer zone. The proposed procedure applies to Abelian theories with matter and with continuous symmetry groups, both on the lattice and in the continuum.

1+24 pages, 4 figures; comments welcome

References in corpus (3)

• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement entropy in d+1 SU(N) gauge theory
• Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

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• Quantum Mechanics in the Infrared
• Rényi Entropy for a $2d$ CFT with a gauge field: $\widehat{\mathrm{SU}}(\mathbf{N}{)}_1$ WZW theory on a branched torus
• Dynamical Edge Modes in Yang-Mills Theory
• Entanglement Entropy across the Lattice-Continuum Correspondence
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach