Random matrices and entanglement entropy of trapped Fermi gases

TL;DR

This paper uses random matrix theory to analytically compute the entanglement entropy of trapped one-dimensional free Fermi gases, confirming results with numerical methods across various regimes.

Contribution

It introduces a novel application of random matrix theory to derive analytic predictions for entanglement entropies in trapped Fermi gases.

Findings

Analytic formulas for Renyi entanglement entropies in harmonic traps

Validation of theoretical predictions with numerical calculations

Insights into entanglement properties across different scaling regimes

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.