Entanglement in the Quantum Hall Matrix Model
Authors
Frenkel, Alexander
Hartnoll, Sean A
Publication Date
2022-05-20Journal Title
JOURNAL OF HIGH ENERGY PHYSICS
ISSN
1029-8479
Publisher
Springer Science and Business Media LLC
Volume
2022
Issue
5
Language
en
Type
Article
This Version
VoR
Metadata
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Frenkel, A., & Hartnoll, S. A. (2022). Entanglement in the Quantum Hall Matrix Model. JOURNAL OF HIGH ENERGY PHYSICS, 2022 (5) https://doi.org/10.1007/JHEP05(2022)130
Abstract
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged U(<jats:italic>N</jats:italic> ) matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain ‘off-diagonal’ matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk ‘area law’ contribution to the entanglement entropy. All of these entropies are regularized by finite <jats:italic>N</jats:italic>.</jats:p>
Keywords
Regular Article - Theoretical Physics, M(atrix) Theories, Chern-Simons Theories, Matrix Models, Non-Commutative Geometry
Identifiers
jhep05(2022)130, 18418
External DOI: https://doi.org/10.1007/JHEP05(2022)130
This record's URL: https://www.repository.cam.ac.uk/handle/1810/337366
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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