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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 $$ \mathcal{N} $$ 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.
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Aspects of higher dimensional quantum Hall effect: Bosonization, entanglement entropy
I give a brief review of higher dimensional quantum Hall effect (QHE) and how one can use a general framework to describe the lowest Landau level dynamics as a noncommutative field theory whose semiclassical limit leads to anomaly free bulk-edge effective actions in any dimension. I then present the case of QHE on complex projective spaces and focus on the entanglement entropy for integer QHE in even spatial dimensions. In the case of đ = 1, a semiclassical analysis shows that the entanglement entropy is proportional to the phase-space area of the entangling surface with a universal overall constant, same for any dimension as well as abelian or nonabelian background magnetic fields. This is modified for higher Landau levels.
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- Award ID(s):
- 1915053
- PAR ID:
- 10463454
- Date Published:
- Journal Name:
- Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2021) - Workshop on Quantum Geometry, Field Theory and Gravity
- Volume:
- 406
- Page Range / eLocation ID:
- 237
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.22323/1.406.0237
