Random matrices and entanglement entropy of trapped Fermi gases
Pasquale CalabreseSISSA and INFN, via Bonomea 265, 34136 Trieste, ItalyPierre Le DoussalCNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex, FranceSatya N. MajumdarCNRS-Université Paris-Sud, LPTMS, UMR8626-Bât 100, 91405 Orsay Cedex, France
2015en
ABI
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We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for R\'enyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretization of the reduced correlation matrix.
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