Lower entropy bounds and particle number fluctuations in a Fermi sea

TL;DR

This paper explores the entanglement, entropy, and particle number fluctuations in a Fermi sea, deriving bounds and analyzing specific cases like quantum Hall electrons at various temperatures.

Contribution

It introduces a simple method to factor a Fermi sea into entangled modes and derives bounds relating entropy and particle fluctuations.

Findings

Derived expressions for entropy and fluctuations at zero and finite temperatures.

Established a lower bound on entropy based on particle number fluctuations.

Analyzed quantum Hall electrons in the lowest Landau level both analytically and numerically.

Abstract

We demonstrate, in an elementary manner, that given a partition of the single particle Hilbert space into orthogonal subspaces, a Fermi sea may be factored into pairs of entangled modes, similar to a BCS state. We derive expressions for the entropy and for the particle number fluctuations of a subspace of a fermi sea, at zero and finite temperatures, and relate these by a lower bound on the entropy. As an application we investigate analytically and numerically these quantities for electrons in the lowest Landau level of a quantum Hall sample.