Momentum space entanglement of interacting fermions

TL;DR

This paper develops a systematic perturbative approach to compute momentum space Rényi entanglement entropy in interacting fermionic systems, revealing universal behaviors in Fermi liquids and superconductors, and suggests experimental measurement methods.

Contribution

It introduces a perturbative expansion for momentum space Rényi entropies applicable at all orders, enabling controlled calculations near the Fermi surface and linking entropy to physical properties.

Findings

Entropy vanishes in the Fermi gas but obeys volume-law in interacting phases.

In Fermi liquids, the entropy is a universal function of quasiparticle residue.

In superconductors, the entropy reflects Cooper pair formation.

Abstract

Momentum space entanglement entropy probes quantum correlations in interacting fermionic phases. It is very sensitive to interactions, obeying volume-law scaling in general, while vanishing in the Fermi gas. We show that the R\'enyi entropy in momentum space has a systematic expansion in terms of the phase space volume of the partition, which holds at all orders in perturbation theory. This permits, for example, the controlled computation of the entropy of thin shells near the Fermi wavevector in isotropic Fermi liquids and BCS superconductors. In the Fermi liquid, the thin shell entropy is a universal function of the quasiparticle residue. In the superconductor, it reflects the formation of Cooper pairs. Momentum space R\'enyi entropies are accessible in cold atomic and molecular gas experiments through a time-of-flight generalization of previously implemented measurement protocols.