Oscillating terms in the Renyi entropy of Fermi liquids

TL;DR

This paper derives a formula for oscillating terms in the Renyi entropy of Fermi liquids, validated by numerical and quantum Monte Carlo calculations, enhancing understanding of entanglement in fermionic systems.

Contribution

It provides a universal formula for oscillating entanglement terms in Fermi liquids, applicable to various geometries and validated by numerical and Monte Carlo methods.

Findings

Excellent agreement between theory and numerical calculations.

Validation of the formula with quantum Monte Carlo data.

Effective description of oscillating entanglement in interacting Fermi liquids.

Abstract

In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and Fermi liquids corresponding to $2k_F$-like oscillations. Our theoretical tools are the one dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface. We compare this term to numerical calculations of entanglement using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find excellent agreement up to moderate interaction strengths.