Decomposition of entanglement entropy in lattice gauge theory

By William Donnelly. 2011

256 citations recorded by the source corpus.

We consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing the edge states in irreducible representations of the gauge group, the entropy of an arbitrary state is expressed as the sum of three positive terms: a term associated with the classical Shannon entropy of the distribution of boundary representations, a term that appears only for non-Abelian gauge theories and depends on the dimension of the boundary representations, and a term representing nonlocal correlations. The first two terms are the entropy of the edge states, and depend only on observables measurable at the boundary. These results are applied to several examples of lattice gauge theory states, including the ground state in the strong coupling expansion of Kogut and Susskind. In all these examples we find that the entropy of the edge states is the dominant contribution to the entanglement entropy.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6a17f0b52b160d462654f1c7e844c2718eb14da1

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “We’ve seen that the presence of a nontrivial central operator indicates that M is not a factor on the code subspace, which in bulk effective field theory is closely related to the presence of gauge symmetry [42, 43, 45, 59–67].”
Entanglement entropy and nonabelian gauge symmetry (2014, methodology): “The calculation of the entanglement entropy proceeds much as in the case of two-dimensional YangMills theory [22].”
Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “The microscopic Hilbert space therefore does not tensor factorize into separate spatial regions [24–28].”
Entwinement and the emergence of spacetime (2014, unknown): “Our procedure of removing the Zn identifications and symmetrizing afterwards recalls methodologies that have been used before to study conventional entanglement entropy in gauge theories (see [51, 52, 53, 54] and references therein).”
Aspects of entanglement entropy for gauge theories (2015, methodology): “Here we will follow the approach discussed in [1] (GST), see also [9], which is also related to the earlier work, [3, 4].”
Geometric entropy and edge modes of the electromagnetic field (2015, methodology): “[32] there is an additional term in the entropy that grows with the dimension of the gauge group, and which might correct for this deficiency.”
Local subsystems in gauge theory and gravity (2016, background): “Here the extended Hilbert space HΣ consists of Wilson loops (or more generally, generalized spin network states [18]) which are allowed to have open ends on the boundary S.”