Status  Confirmed 
Seminar Series  SEMLPTHE 
Subjects  condmat.statmech,hepth,mathph 
Date  Friday 25 January 2019 
Time  11:00 
Institute  LPTHE 
Seminar Room  Bibliothèque 
Speaker's Last Name  LacroixAChezToine 
Speaker's First Name  Bertrand 
Speaker's Email Address  
Speaker's Institution  LPTMS Orsay 
Title  Exact entanglement entropy for noninteracting fermions in rotation 
Abstract  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 noninteracting 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 noninteracting fermions in two dimensions trapped by an harmonic potential and rotating at constant frequency. I will first show that the groundstate of this model can be mapped to the socalled 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. LacroixAChezToine, S. N. Majumdar and G. Schehr, Entanglement Entropy and Full Counting Statistics for 2dRotating Trapped Fermions, arXiv preprint 1809.05835, (2018). 
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