Momentum space entanglement of interacting fermions

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 Renyi 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 wave vector 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 Renyi entropies are accessible in cold atomic and molecular gas experiments through a time-of-flight generalization of previously implemented measurement protocols.

Automated summary

Momentum space entanglement entropy is sensitive to interactions and can probe quantum correlations in interacting fermionic phases. It follows volume-law scaling in general, but vanishes in the Fermi gas. The Renyi entropy in momentum space can be systematically expanded in terms of the phase space volume of the partition, allowing for controlled computation of entropy near the Fermi wave vector in isotropic Fermi liquids and BCS superconductors. It can be accessed in cold atomic and molecular gas experiments through a time-of-flight generalization of previous measurement protocols.