Random matrices and entanglement entropy of trapped Fermi gases

Abstract

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 Renyi 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 discretisation of the reduced correlation matrix.

arXiv comment12 pages, 6 figures, one subsection added in v2

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• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"