Equilibrium and nonequilibrium entanglement properties of two- and three-dimensional Fermi gases

Abstract

We investigate the entanglement properties of the equilibrium and nonequilibrium quantum dynamics of two-dimensional (2D) and three-dimensional (3D) Fermi gases, by computing entanglement entropies of extended space regions, which generally show multiplicative logarithmic corrections to the leading power-law behaviors, corresponding to the logarithmic corrections to the area law. We consider 2D and 3D Fermi gases of $N$ particles constrained within a limited space region, for example, by a hard-wall trap, at equilibrium at $T=0$, i.e., in their ground state, and compute the first few terms of the asymptotic large-$N$ behaviors of entanglement entropies and particle fluctuations of subsystems with some convenient geometries, which allow us to significantly extend their computation. Then we consider their nonequilibrium dynamics after instantaneously dropping the hard-wall trap, which allows the gas to expand freely. We compute the time dependence of the von Neumann entanglement entropy of space regions around the original trap. We show that at small time it is characterized by the relation $S\ensuremath{\approx}{\ensuremath{\pi}}^{2}V/3$ with the particle variance, and multiplicative logarithmic corrections to the leading power law, i.e., $S\ensuremath{\sim}{t}^{1\ensuremath{-}d}\mathrm{ln}(1/t)$.