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Mathematical open problems in Projected Entangled Pair States
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Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.
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Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
Two-dimensional many-body-localized systems with an on-site abelian symmetry are shown to carry a topological index in the (generalized) third cohomology group of the symmetry group, robust to local perturbations.
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