Mathematics Colloquia and Seminars

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Projected Entangled Pairs States (PEPS) constitute a class of 2-dimensional quantum many-body states, and they are believed to describe many of the interesting features of quantum spin models at low temperature. One the crucial property in this setting is whether a state is a groundstate of a local Hamiltonian with a system-size independent spectral gap - the difference between its two lowest eigenvalues.

I will present some recent results about the relationship between the so called boundary Hamiltonian of a PEPS and the spectral gap. Namely, for 2D PEPS it is possible to define a 1-dimensional "boundary Hamiltonian", which describes the entanglement structure of the groundstate. I will show that if this Hamiltonian has finite-range interactions, then the system is gapped.