2020/10/31 by Isaac H. Kim · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.str-el #math-ph #math.MP
paper · pdf · doi:10.1103/physrevx.11.021039
published as Phys. Rev. X 11, 021039 (2021) · 61 pages, 7 figures, ~200 in-line figures. Added the toric code example and a discussion about an efficient tensor network construction. More detailed explanation added in Section II
arxiv created 2021/02/03 · arxiv updated 2021/05/26
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can 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 conjecture 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-linear constraints -- all of which follow from the entropy scaling law straightforwardly -- must be consistent with some global state on an infinite lattice. Moreover, we derive a closed-form expression for the maximum entropy density compatible with those marginals, deriving a variational upper bound on the thermodynamic free energy. Our construction's main assumptions are satisfied exactly by solvable models of topological order and approximately by finite-temperature Gibbs states of certain quantum spin Hamiltonians.