Minimally entangled microcanonical states

A recent conjecture inspired by black hole physics suggests that generic quantum many-body systems should admit finite-energy-density states with area-law entanglement and an energy variance that vanishes in the thermodynamic limit. This prediction is in sharp contradiction with intuition since finite-energy-density eigenstates of such systems exhibit volume-law entanglement. To test this hypothesis, we study a chaotic quantum spin chain using a numerical algorithm to minimize von-Neumann and Rényi entanglement entropies within narrow microcanonical energy windows. Our focus is on determining the emergent scaling relations governing how the minimal entanglement varies with window width. We comment on implications for the equivalence of quantum statistical ensembles and on the relation to quantum many-body scars.