Universality in the full counting statistics of trapped fermions

TL;DR

This paper uncovers universal statistical behaviors in the particle number distribution of trapped fermions, linking quantum many-body physics with random matrix theory, and confirming these universality features through scaling analyses.

Contribution

It demonstrates that the full counting statistics of a trapped Fermi gas exhibit universal limits described by Gaussian unitary ensembles, connecting quantum statistics with random matrix universality.

Findings

Universal behavior in bulk and edge regions of trapped fermions

Full counting statistics match Gaussian unitary ensemble limits

Scaling of fluctuations and entanglement entropy confirms universality

Abstract

We study the distribution of particle number in extended subsystems of a one-dimensional non-interacting Fermi gas confined in a potential well at zero temperature. Universal features are identified in the scaled bulk and edge regions of the trapped gas where the full counting statistics are given by the corresponding limits of the eigenvalue statistics in Gaussian unitary random matrix ensembles. The universal limiting behavior is confirmed by the bulk and edge scaling of the particle number fluctuations and the entanglement entropy.