Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states

Abstract

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 $\mathcal{N}=4$ 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.

57 pages, 5 figures

References in corpus (15)

• Quantum Noise as an Entanglement Meter
• Universality of corner entanglement in conformal field theories
• Entwinement and the emergence of spacetime
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Anatomy of bubbling solutions
• Random matrices and entanglement entropy of trapped Fermi gases
• Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Holographic entanglement entropy and the internal space
• Fluctuations and Entanglement spectrum in quantum Hall states
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Entanglement in the Quantum Hall Matrix Model
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Target space entanglement in a matrix model for the bubbling geometry
• Matrix Model Maps and Reconstruction of AdS SUGRA Interactions

Cited by in corpus (1)

• Target Space Entanglement in Quantum Mechanics of Fermions and Matrices