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arxiv 1706.07329 v2 pith:DDKOEAVO submitted 2017-06-22 cond-mat.str-el quant-ph

A generalization of the injectivity condition for Projected Entangled Pair States

Andras Molnar , Yimin Ge , Norbert Schuch , J. Ignacio Cirac This is my paper
classification cond-mat.str-el quant-ph
keywords statespepssemi-injectivefamilygroundprojectedakltclass
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We introduce a family of tensor network states that we term semi-injective Projected Entangled-Pair States (PEPS). They extend the class of injective PEPS and include other states, like the ground states of the AKLT and the CZX models in square lattices. We construct parent Hamiltonians for which semi-injective PEPS are unique ground states. We also determine the necessary and sufficient conditions for two tensors to generate the same family of such states in two spatial dimensions. Using this result, we show that the third cohomology labeling of Symmetry Protected Topological phases extends to semi-injective PEPS.

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  1. Mapping twist fields to local operators via tensor networks

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    Constructs explicit physical local operators whose expectation values match twist field actions in MPS, exact in the injectivity limit and at the center of orthogonality, with numerical tests in the transverse-field I...