A Generalized Injectivity Condition for PEPS
February 20th, 2017 ANDRAS MOLNAR Max-Planck-Institut für Quantenoptik, Garching

Projected Entangled Pair States (PEPS) is an ansatz believed to be suitable for analytical and numerical investigation of ground states of many-body Hamiltonians. To design a PEPS that admits certain (local) symmetries one has to understand when two different PEPS tensors give rise to the same state. This question in the full generality is however undecidable, it is therefore important to find relevant classes of tensors for which it can be answered. One such class is injcetive PEPS. Two injective PEPS describe the same state if and only if their tensors are related with a gauge transformation on the virtual space. Here we provide a generalisation of this class. This generalisation includes states that fail to be injective for purely geometrical reasons (so called corner problem). We show under which condition can two such states be equal. We also show that symmetries give rise to invertible Matrix Product Operators (MPO) on the boundary degrees of freedom. These MPOs can be used to assign an element of the third cohomology of the symmetry group to the state the same way as in the classification of the Symmetry Protected Topological (SPT) phases.

Seminar, February 20, 2017, 12:00. Seminar Room

Hosted by Prof. Antonio Acín