Entanglement in the Quantum Hall Matrix Model

Frenkel, Alexander; Hartnoll, Sean A.

doi:10.1007/jhep05(2022)130

Entanglement in the Quantum Hall Matrix Model

Journal Article · Fri May 20 00:00:00 EDT 2022 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep05(2022)130· OSTI ID:1976477

Frenkel, Alexander ^[1]; Hartnoll, Sean A. ^[2]

Stanford University, CA (United States); Stanford Univ., CA (United States)
University of Cambridge (United Kingdom)

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(N) 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 N.

View Accepted Manuscript (DOE)

Research Organization:: Stanford University, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); Science and Technology Facilities Council (STFC); Simons Investigator; USDOE Office of Science (SC)

Grant/Contract Number:: SC0018134

OSTI ID:: 1976477

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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