Date of Award
Fall 1-1-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
First Advisor
Cheng, Meng
Abstract
Symmetry and its anomaly constrain a system's dynamics and provide a universal characterization of its behaviors. It serves as a powerful tool to understand exotic phases of matter, especially symmetry-protected topological (SPT) orders. The notion of generalized symmetries requires extending our previous understanding of topological phases to those enriched by fusion category symmetries, yet new mathematical formalism is needed to apply unitary fusion category symmetries to a microscopic system. This thesis starts with a model-independent description of an abstract spin chain viewed as a net of C*-algebras. From a microscopic SymTFT, categorical structures describing symmetry and symmetry charges can be extracted. This proof is followed by a general fixed-point lattice construction of (1+1)d SPTs with unitary fusion category symmetries, realized in a tensor-product Hilbert space with an “onsite” matrix-product-operator (MPO) version of the Hopf C*-algebra symmetry operators. Within this construction, it is addressed that the UV description of an anomaly-free fusion category symmetry must include the fiber functor, giving rise to a local symmetry action, a charge category and a trivial phase. An alternative characterization of SPT phases using the Q-systems in the charge category is proposed and proved.
Recommended Citation
YANG, XINPING, "(1+1)d Topological Phases Enriched with Fusion Category Symmetries" (2025). Yale Graduate School of Arts and Sciences Dissertations. 1882.
https://elischolar.library.yale.edu/gsas_dissertations/1882