An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
A remark on gapped domain walls between topological phases
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abstract
We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics based on works of Davydov, M\"uger, Nikshych and Ostrik. In particular, we identify their tunneling matrix and a coupling matrix of Rehren, and show that their conjecture does not hold.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
- Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries