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Entanglement in the Quantum Hall Matrix Model

Published version
Peer-reviewed

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Authors

Frenkel, A 
Hartnoll, SA 

Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pCharacterizing 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:italicN</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:italicN</jats:italic>.</jats:p>

Description

Keywords

Regular Article - Theoretical Physics, M(atrix) Theories, Chern-Simons Theories, Matrix Models, Non-Commutative Geometry

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1029-8479
1029-8479

Volume Title

2022

Publisher

Springer Science and Business Media LLC