Renyi Entropy of the Interacting Fermi Liquid

TL;DR

This study uses quantum Monte Carlo methods to analyze how Renyi entropies in interacting Fermi liquids depend on system size, interaction strength, and entropy order, revealing interaction-induced increases and modifications in scaling laws.

Contribution

It provides the first detailed quantum Monte Carlo analysis of Renyi entropies in interacting Fermi liquids, exploring their dependence on system size, interaction strength, and entropy order.

Findings

Interactions increase Renyi entropies.

Interactions modify the scaling law prefactors.

The $L ext{log}L$ scaling origin is linked to the swap operator.

Abstract

We perform quantum Monte Carlo calculations to determine how the Renyi entropies, $S_n$, of the interacting Fermi liquid depend on Renyi order, $n$, and scale as a function of system size, $L$. Using the swap operator and an accurate Slater-Jastrow wave function, we compute Renyi entropies for spinless fermions interacting via the Coulomb and modified P\"{o}schl-Teller potentials across a range of correlation strengths. Our results show that interactions increase the Renyi entropies and increase the prefactor of their scaling laws. The relationships between Renyi entropies of different order $n$ are also modified. Additionally, we investigate the effect of the swap operator on the Fermi liquid wave function to determine the source of the $L\log L$ scaling form.