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

Oscillating terms in the Renyi entropy of Fermi liquids