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

Sumit R. Das, Shaun Hampton, Sinong Liu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 S3. In this latter context, the entanglement we consider is an entanglement in target space. We comment on possible implications to gauge-gravity duality.

Original languageEnglish
Article number46
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).


  • Field Theories in Lower Dimensions
  • Gauge-Gravity Correspondence
  • Matrix Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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