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SUMMARY:Isaac Kim (Univeristy of Sydney)
DTSTART:20210222T210000Z
DTEND:20210222T221500Z
DTSTAMP:20260404T150744Z
UID:HET/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HET/8
 /">Entropy scaling law and the quantum (and classical) marginal problem</a
 >\nby Isaac Kim (Univeristy of Sydney) as part of Purdue HET\n\n\nAbstract
 \nQuantum (and classical) many-body states that appear in physics often ob
 ey an entropy scaling law\, meaning that an entanglement entropy of a subs
 ystem can be expressed as a sum of terms that scale linearly with its volu
 me and area\, plus a correction term that is independent of its size. We c
 onjecture 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 conject
 ure for translationally invariant systems in two spatial dimensions. Speci
 fically\, we prove that a translationally invariant marginal obeying three
  non-linear constraints -- all of which follow from the entropy scaling la
 w straightforwardly -- must be consistent with some global state on an inf
 inite lattice. Moreover\, we derive a closed-form expression for the maxim
 um entropy density compatible with those marginals\, deriving a variationa
 l upper bound on the thermodynamic free energy. Our construction's main as
 sumptions are satisfied exactly by solvable models of topological order an
 d approximately by finite-temperature Gibbs states of certain quantum spin
  Hamiltonians. To the best of our knowledge\, this is the first nontrivial
  solution to the quantum marginal problem in a many-body setting that lies
  strictly outside the framework of mean-field theory.\n
LOCATION:https://stable.researchseminars.org/talk/HET/8/
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