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Revisiting entanglement entropy of lattice gauge theories

  • Ling-Yan Hung
  • Yidun Wan
Open Access
Regular Article - Theoretical Physics

Abstract

It is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model [1] which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.

Keywords

Lattice Gauge Field Theories Gauge Symmetry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina
  2. 2.Collaborative Innovation Center of Advanced MicrostructuresFudan UniversityShanghaiChina
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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