Locality at the boundary implies gap in the bulk for 2D PEPS

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Michael J. Kastoryano, Angelo Lucia, David Perez-Garcia

Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit. The proof employs the martingale method of nearly commuting projectors, and exploits a result of Araki on the robustness of one dimensional Gibbs states. Our result provides one of the first rigorous connections between boundary theories and dynamical properties in an interacting many body system. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk.
OriginalsprogEngelsk
TidsskriftCommunications in Mathematical Physics
Vol/bind366
Udgave nummer3
Sider (fra-til)895–926
ISSN0010-3616
DOI
StatusUdgivet - 2019

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