Matrix product operator symmetries and intertwiners for topological and critical lattice models

Abstract: Projected entangled pair state (PEPS) descriptions of (2+1)d topologically ordered states are characterized by non-local matrix product operator (MPO) symmetries on the entanglement degrees of freedom of the PEPS tensors. Various explicit tensor network representations and their symmetries have been known for a long time, examples being G-injective and string-net PEPS. In this talk, based on our recent work (arXiv:2008.11187), I will synthesize and generalize these results by showing that the consistency conditions for MPO symmetries amount to the defining equations of a bimodule category, thereby showing that the classification of these PEPS and MPO symmetries amounts to the classification of the data of a bimodule category. Different PEPS representations of the same state can be related by an MPO intertwiner, which can be thought of as a generalized gauge transformation on the virtual level, providing an important step towards a general fundamental theorem of PEPS. Additionally, these new PEPS representations allow us to construct tensor network representations of domain walls between different topological phases. Finally, all these results have an immediate application to critical lattice models described by CFT, and I will illustrate this by giving an example of orbifolding or simple current extension on the lattice.

statistical mechanicsHEP - theorycomputational physicsquantum physics

Audience: researchers in the topic

HEP-tensor network seminars

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