University of Cambridge > Talks.cam > CQIF Seminar > Locality at the boundary implies gap in the bulk for 2D PEPS

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

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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 Gibbs state of a local Hamiltomian on the virtual indices with interactions decaying faster than exponentially in the distance, 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. If time permits, we will discuss some recent work on relating PEPS to certain O(n) Loop models.

This talk is part of the CQIF Seminar series.

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