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Title: On the definition of entanglement entropy in lattice gauge theories
Authors: Aoki, Sinya
Iritani, Takumi
Nozaki, Masahiro
Numasawa, Tokiro
Shiba, Noburo
Tasaki, Hal
Author's alias: 入谷, 匠
Keywords: Lattice Gauge Field Theories
Gauge Symmetry
Issue Date: 26-Jun-2015
Publisher: Springer Berlin Heidelberg
Journal title: Journal of High Energy Physics
Volume: 2015
Issue: 6
Thesis number: 187
Abstract: We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z(N) gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z(N) gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
Rights: JHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.0
DOI(Published Version): 10.1007/JHEP06(2015)187
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