The entanglement spectrum and R\'enyi entropies of non-relativistic conformal fermions

TL;DR

This paper non-perturbatively analyzes the Renyi entropies and entanglement spectrum of strongly coupled three-dimensional fermion systems at unitarity, revealing universal features and the impact of pairing correlations on entanglement properties.

Contribution

It provides the first non-perturbative lattice calculations of Renyi entropies for unitary fermions and explores the entanglement spectrum across coupling regimes, highlighting universal behaviors.

Findings

Sub-leading entanglement entropy behavior is affected by strong pairing.

Onset of sub-leading regime occurs at small subsystem sizes (x=2-4).

Low-lying entanglement spectrum shows scale invariance and eigenvalue crossing.

Abstract

We characterize non-perturbatively the R\'enyi entropies of degree n=2,3,4, and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit. We carry out our calculations using lattice methods devised recently by us. Our results show the effect of strong pairing correlations on the entanglement entropy, which modify the sub-leading behavior for large subsystem sizes (as characterized by the dimensionless parameter x=kF L_A, where kF is the Fermi momentum and L_A the linear subsystem size), but leave the leading order unchanged relative to the non-interacting case. Moreover, we find that the onset of the sub-leading asymptotic regime is at surprisingly small x=2-4. We provide further insight into the entanglement properties of this system by analyzing the spectrum of the entanglement Hamiltonian of the two-body problem from weak to strong coupling. The low-lying entanglement spectrum displays clear features as the strength of the coupling is varied, such as eigenvalue crossing, a sharp change in the Schmidt gap, and scale invariance at unitarity. Beyond the low-lying component, the spectrum appears as a quasi-continuum distribution, for which we present a statistical characterization; we find, in particular, that the mean shifts to infinity as the coupling is turned off, which indicates that that part of the spectrum represents non-perturbative contributions to the entanglement Hamiltonian. In contrast, the low-lying entanglement spectrum evolves to finite values in the noninteracting limit. The scale invariance of the unitary regime guarantees that our results are universal features intrinsic to 3D quantum mechanics and represent a well-defined prediction for ultracold atom experiments, which were recently shown to have direct access to the entanglement entropy.