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Résumé |
Bipartite entanglement entropy is a convenient observable to characterise
critical and topological phases of matter. Despite numerous recent efforts, it
remains a challenge to obtain both analytical results as well as experimental
measurements of this quantity, even for simple systems. Some progress has been
achieved recently by realising that in specific cases, e.g. for N non-interacting
particles, the entanglement entropy is directly proportional to the number vari-
ance in the large N limit [1]. This number variance corresponds to the variance
of the number of particles in a given domain, an observable much easier to
measure experimentally. In this talk I will present a system of non-interacting
fermions in two dimensions trapped by an harmonic potential and rotating at
constant frequency. I will first show that the ground-state of this model can be
mapped to the so-called complex Ginibre ensemble of Random Matrix Theory
(RMT). Then I will use RMT techniques to obtain both the entanglement en-
tropy and the number variance for the fermions in a disk [2]. This computation
remains valid for any number N of particles. In the large N limit, we show that
the proportionality between number variance and entanglement entropy holds
in the bulk, i.e. far enough from the edge of the density while it breaks down
at this edge.
References :
[1] I. Klich, L. Levitov, Quantum noise as an entanglement meter, Phys. Rev.
Lett. 102, 100502 (2009);
[2] B. Lacroix-A-Chez-Toine, S. N. Majumdar and G. Schehr, Entanglement
Entropy and Full Counting Statistics for 2d-Rotating Trapped Fermions,
arXiv preprint 1809.05835, (2018).
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