Convexity of the entanglement energy of SU()-symmetric fermions with attractive interactions
arXiv:1410.0654 · doi:10.1103/PhysRevLett.114.050402
Abstract
The positivity of the probability measure of attractively interacting systems of -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 -th Rényi entanglement entropy derived recently, we prove non-perturbative analytic relations for the entanglement energies of those systems defined via where is the extent of the imaginary time direction and where 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.
arXiv comment4 pages, 3 figures; original replaced with corrected version. Merges published version and associated erratum
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