BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Isaac Kim (Univeristy of Sydney) DTSTART:20210222T210000Z DTEND:20210222T221500Z DTSTAMP:20260423T004820Z UID:HET/8 DESCRIPTION:Title: Entr opy scaling law and the quantum (and classical) marginal problem\nby I saac Kim (Univeristy of Sydney) as part of Purdue HET\n\n\nAbstract\nQuant um (and classical) many-body states that appear in physics often obey an e ntropy scaling law\, meaning that an entanglement entropy of a subsystem c an be expressed as a sum of terms that scale linearly with its volume and area\, plus a correction term that is independent of its size. We conjectu re that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions\, obeying the same entropy scaling law locally. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. Specifically \, we prove that a translationally invariant marginal obeying three non-li near constraints -- all of which follow from the entropy scaling law strai ghtforwardly -- must be consistent with some global state on an infinite l attice. Moreover\, we derive a closed-form expression for the maximum entr opy density compatible with those marginals\, deriving a variational upper bound on the thermodynamic free energy. Our construction's main assumptio ns are satisfied exactly by solvable models of topological order and appro ximately by finite-temperature Gibbs states of certain quantum spin Hamilt onians. To the best of our knowledge\, this is the first nontrivial soluti on to the quantum marginal problem in a many-body setting that lies strict ly outside the framework of mean-field theory.\n LOCATION:https://researchseminars.org/talk/HET/8/ END:VEVENT END:VCALENDAR