Spring 2014

MPO-injectivity and Topologically Ordered PEPS

Wednesday, April 23rd, 2014 1:30 pm2:30 pm

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It is well known that many RG-fixed point states with topological order such as the quantum double models of Kitaev and the string net models of Levin and Wen can exactly be represented as PEPS. In this talk we will discuss how the topologically ordered properties of the state manifest themselves in the PEPS representation, even for states that are not exactly at the RG-fixed point. For the case of the quantum doubles, it is well known that this gives rise to the notion of G-injectivity, as was first introduced by Schuch et al. In this case, the PEPS tensors are invariant under the action of the discrete group G at the virtual level. This construction was recently generalised to models where the symmetry group is twisted by a 3-cocylce by Buerschaper. We further extend this formalism by showing how to suitably redefining the notion of injectivity when the invariance of the PEPS tensors is encoded in general MPOs, and we illustrate that the general Levin-Wen string nets are exactly of this form.