Entanglement entropy and phase space density: lowest Landau levels and 1/2 BPS states

A bstract We consider the entanglement entropy of an arbitrary subregion in a system of N non-relativistic fermions in 2+1 dimensions in Lowest Landau Level (LLL) states. Using the connection of these states to those of an auxiliary 1 + 1 dimensional fermionic system, we derive an expression for the...

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Bibliographic Details
Published in:The journal of high energy physics 2022-06, Vol.2022 (6), p.46-48, Article 46
Main Authors: Das, Sumit R., Hampton, Shaun, Liu, Sinong
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Condensed Matter
Elementary Particles
Entropy
Fermions
Field Theories in Lower Dimensions
Gauge-Gravity Correspondence
High energy physics
High Energy Physics - Theory
Mathematical analysis
Matrix Models
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Hall effect
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Space density
String Theory
Yang-Mills theory
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Summary:A bstract We consider the entanglement entropy of an arbitrary subregion in a system of N non-relativistic fermions in 2+1 dimensions in Lowest Landau Level (LLL) states. Using the connection of these states to those of an auxiliary 1 + 1 dimensional fermionic system, we derive an expression for the leading large- N contribution in terms of the expectation value of the phase space density operator in 1 + 1 dimensions. For appropriate subregions the latter can replaced by its semiclassical Thomas-Fermi value, yielding expressions in terms of explicit integrals which can be evaluated analytically. We show that the leading term in the entanglement entropy is a perimeter law with a shape independent coefficient. Furthermore, we obtain analytic expressions for additional contributions from sharp corners on the entangling curve. Both the perimeter and the corner pieces are in good agreement with existing calculations for special subregions. Our results are relevant to the integer quantum Hall effect problem, and to the half-BPS sector of N = 4 Yang Mills theory on S 3 . In this latter context, the entanglement we consider is an entanglement in target space. We comment on possible implications to gauge-gravity duality.
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP06(2022)046