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Mathematical open problems in Projected Entangled Pair States

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arxiv 1903.09439 v2 pith:3XYZKM6M submitted 2019-03-22 math-ph cond-mat.str-elmath.MPquant-ph

classification math-phcond-mat.str-elmath.MPquant-ph
keywords mathematicalstatesentangledpairpepsprojectedaudiencebody
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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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  1. Classification of symmetry-protected topological phases in two-dimensional many body-localized systems

    cond-mat.dis-nn 2019-08 conditional novelty 6.0 of 10

    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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