A remark on matrix product operator algebras, anyons and subfactors

Abstract

We show that the mathematical structures in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete are the same as those of flat symmetric bi-unitary connections and the tube algebra in subfactor theory. More specifically, a system of flat symmetric bi-unitary connections arising from a subfactor with finite index and finite depth satisfies all their requirements for tensors and the tube algebra for such a subfactor and the anyon algebra for such tensors are isomorphic up to the normalization constants. Furthermore, the matrix product operator algebras arising from tensors corresponding to possibly non-flat symmetric bi-unitary connections are isomorphic to those arising from flat symmetric bi-unitary connections for subfactors.

three explanatory paragraphs added

References in corpus (2)

• Locality at the boundary implies gap in the bulk for 2D PEPS
• (2+1)-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants

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