Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state

TL;DR

This paper analyzes the entanglement between spin components in the BCS ground state, revealing that entanglement entropy correlates with pairing energy, electron number fluctuations, and can be modeled by a generalized Gibbs ensemble.

Contribution

It introduces a detailed analysis of the entanglement spectrum in the BCS ground state and links entanglement entropy to physical quantities like pairing energy and number fluctuations.

Findings

Entanglement spectrum modeled by a generalized Gibbs ensemble.

Entanglement entropy proportional to pairing energy and Fermi surface electrons.

Entanglement entropy proportional to spin component number fluctuations.

Abstract

We study entanglement between the spin components of the Bardeen-Cooper-Schrieffer (BCS) ground state by calculating the full entanglement spectrum and the corresponding von Neumann entanglement entropy. The entanglement spectrum is effectively modeled by a generalized Gibbs ensemble (GGE) of non-interacting electrons, which may be approximated by a canonical ensemble at the BCS critical temperature. We further demonstrate that the entanglement entropy is jointly proportional to the pairing energy and to the number of electrons about the Fermi surface (an area law). Furthermore, the entanglement entropy is also proportional to the number fluctuations of either spin component in the BCS state.