Entanglement entropy and particle number cumulants of disordered fermions

I. S. Burmistrov, K. S. Tikhonov, I. V. Gornyi, A. D. Mirlin

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2 Citations (Scopus)

Abstract

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

Original languageEnglish
Pages (from-to)140-156
Number of pages17
JournalAnnals of Physics
Volume383
DOIs
Publication statusPublished - Aug 2017
Externally publishedYes

Keywords

  • Anderson transition
  • Entanglement

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