Entanglement Entropy and Full Counting Statistics for $2d$-Rotating Trapped Fermions

Bertrand Lacroix-A-Chez-Toine; Satya N. Majumdar; Gregory Schehr

doi:10.1103/PhysRevA.99.021602

paper

Entanglement Entropy and Full Counting Statistics for $2 d$ -Rotating Trapped Fermions

arXiv:1809.05835 · doi:10.1103/PhysRevA.99.021602

Abstract

We consider $N$ non-interacting fermions in a $2 d$ harmonic potential of trapping frequency $ω$ and in a rotating frame at angular frequency $Ω$ , with $0 < ω - Ω ≪ ω$ . At zero temperature, the fermions are in the non-degenerate lowest Landau level and their positions are in one to one correspondence with the eigenvalues of an $N \times N$ complex Ginibre matrix. For large $N$ , the fermion density is uniform over the disk of radius $N$ centered at the origin and vanishes outside this disk. We compute exactly, for any finite $N$ , the Rényi entanglement entropy of order $q$ , $S_{q} (N, r)$ , as well as the cumulants of order $p$ , $⟨ N_{r}^{p} ⟩_{c}$ , of the number of fermions $N_{r}$ in a disk of radius $r$ centered at the origin. For $N ≫ 1$ , in the (extended) bulk, i.e., for $0 < r / N < 1$ , we show that $S_{q} (N, r)$ is proportional to the number variance $Var (N_{r})$ , despite the non-Gaussian fluctuations of $N_{r}$ . This relation breaks down at the edge of the fermion density, for $r \approx N$ , where we show analytically that $S_{q} (N, r)$ and $Var (N_{r})$ have a different $r$ -dependence.

arXiv comment6 pages + 7 pages (Supplementary material), 2 Figures

Entanglement Entropy and Full Counting Statistics for $2 d$ -Rotating Trapped Fermions

Abstract

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Cited by in corpus (38)

Entanglement Entropy and Full Counting Statistics for 2d-Rotating Trapped Fermions

Abstract

References in corpus (34)

Cited by in corpus (38)

Entanglement Entropy and Full Counting Statistics for $2 d$ -Rotating Trapped Fermions