Projector Matrix Product Operators, Anyons and Higher Relative Commutants of Subfactors

Abstract

A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional topological order and anyons. In their work, they have a special projection called a projector matrix product operator. We prove that the range of this projection of length k is naturally identified with the k-th higher relative commutant of the subfactor arising from the bi-unitary connection. This gives a further connection between 2-dimensional topological order and subfactor theory.

arXiv comment17 pages, improved exposition

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Cited by in corpus (4)

• Two-dimensional topological order and operator algebras
• Quantum cellular automata and categorical dualities of spin chains
• Anyonic Chains -- $\alpha$-Induction -- CFT -- Defects -- Subfactors
• A characterization of a finite-dimensional commuting square producing a subfactor of finite depth