Entanglement and particle correlations of Fermi gases in harmonic traps

TL;DR

This paper analyzes quantum correlations, entanglement, and particle fluctuations in large noninteracting Fermi gases confined by harmonic traps across different dimensions, revealing universal scaling laws and relations.

Contribution

It provides explicit formulas for entanglement entropies and demonstrates universal large-N scaling behaviors in trapped Fermi gases across dimensions.

Findings

Half-space entanglement entropy scales as N^(d-1)/d ln N.

Large-N relation between entanglement entropy and particle variance holds universally.

Derived explicit coefficients for entanglement entropy in 1D, 2D, and 3D.

Abstract

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.