BIMSA >
BIMSA TQFT and Higher Symmetries Seminar
On-Site Realization of Anomaly-Free Fusion Category Symmetry and Local Ground State Degeneracy in a Fixed-Point Model
On-Site Realization of Anomaly-Free Fusion Category Symmetry and Local Ground State Degeneracy in a Fixed-Point Model
Organizers
Speaker
Chenqi Meng
Time
Tuesday, March 11, 2025 9:45 AM - 11:30 AM
Venue
A3-2-301
Online
Zoom 468 248 1222
(BIMSA)
Abstract
To impose a group-like, anomaly-free internal symmetry on a lattice, one must assign an on-site action to the symmetry operator--this local structure ensures that the trivial symmetric phase comprises states smoothly connected to a product state via finite-depth symmetric local unitaries. For an anomaly-free fusion category symmetry, it is equally crucial to specify the local symmetry action on the tensor product Hilbert space. This can be encapsulated by a fiber functor, which maps objects in the fusion category to virtual bonds of the corresponding symmetry matrix product operators [Molnar22]. Once this fiber functor is fixed, it simultaneously determines the local symmetry action, the category of symmetry charges, and the trivial symmetric phase.
To realize symmetric fusion category phases, we study the local ground-state degeneracy on an open disk in the fixed-point model proposed by [Inamura21]. We show that a symmetric phase can be identified with a Q-system in the charge category, which reduces to a matrix algebra when the symmetry is "forgotten". We further prove the equivalence between fiber functor-based and Q-system-based classifications of fusion category symmetric phases. As an example, we present an explicit microscopic realization of the three $\mathrm{Rep}(D_8)$ SPT phases (including the trivial one) and demonstrate the $S_3$-duality among these phases on the lattice.
To realize symmetric fusion category phases, we study the local ground-state degeneracy on an open disk in the fixed-point model proposed by [Inamura21]. We show that a symmetric phase can be identified with a Q-system in the charge category, which reduces to a matrix algebra when the symmetry is "forgotten". We further prove the equivalence between fiber functor-based and Q-system-based classifications of fusion category symmetric phases. As an example, we present an explicit microscopic realization of the three $\mathrm{Rep}(D_8)$ SPT phases (including the trivial one) and demonstrate the $S_3$-duality among these phases on the lattice.