Convexity of the entanglement energy of SU($2N$)-symmetric fermions with attractive interactions

TL;DR

This paper proves a convexity property of the entanglement energy in SU(2N)-symmetric fermionic systems with attractive interactions, based on positivity of the probability measure, applicable across various parameters and conditions.

Contribution

It introduces a non-perturbative analytic relation for entanglement energies in SU(2N) fermions, extending convexity properties to a broad class of systems with attractive interactions.

Findings

Proves convexity of entanglement energy for these systems.

Derives exact analytic relations for entanglement energies.

Results hold for all subsystem sizes, particle numbers, dimensions, and trapping potentials.

Abstract

The positivity of the probability measure of attractively interacting systems of $2N$-component fermions enables the derivation of an exact convexity property for the ground-state energy of such systems. Using analogous arguments, applied to path-integral expressions for the $n$-th R\'enyi entanglement entropy $S^{}_n$ derived recently, we prove non-perturbative analytic relations for the entanglement energies $\mathcal E^{}_n$ of those systems defined via $\mathcal{E}^{}_n \equiv \frac{n-1}{n}T S^{}_n + F$ where $\beta = 1/T$ is the extent of the imaginary time direction and $-\beta F = \ln \mathcal Z$ where $\mathcal Z$ is the partition sum appropriate to the temperature. These relations are valid for all sub-system sizes, particle numbers and dimensions, and in arbitrary external trapping potentials.