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

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 Rényi 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.

Comments: 4 pages, 3 figures; original replaced with corrected version. Merges published version and associated erratum