Momentum space entanglement of interacting fermions

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

10 pages, 4 figures

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• New Trends in Density Matrix Renormalization
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Momentum-space analysis of multipartite entanglement at quantum phase transitions

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• A One-Dimensional Electron Gas Coupled to Light
• Holographic entanglement renormalisation for fermionic quantum matter