3 problems

Boundary Gibbs-state conjecture. The parent Hamiltonian of the PEPS is gapped if and only if the boundary states can be written as Gibbs states of one-dimensional short-range Hamil…

Let $\Lambda$ be the underlying lattice, let $A\subset\Lambda$ be any rectangular region, and let $H_A$ denote the corresponding parent Hamiltonian restricted to $A$. A boundary st…

Let a PEPS have a bulk parent Hamiltonian and an associated one-dimensional boundary Hamiltonian. Bulk-boundary gap conjecture. The bulk parent Hamiltonian of the PEPS is gapped if…