BIMSA > BIMSA TQFT and Higher Symmetries Seminar A Lattice Realization of Topological Gapped Boundaries via Lagrangian Algebras
A Lattice Realization of Topological Gapped Boundaries via Lagrangian Algebras
Organizers
Ansi Bai , Hank Chun-Hao Chen , Liang Kong , Yi Long Wang , Zhi Hao Zhang , Hao Zheng
Speaker
Mu Li
Time
Tuesday, June 3, 2025 9:45 AM - 11:30 AM
Venue
A3-2-301
Online
Zoom 388 528 9728 (BIMSA)
Abstract
Boundaries, exhibiting remarkable properties such as holographic duality, constitute essential features of topological orders. The mathematical framework of anyon condensation establishes that gapped boundaries correspond to Lagrangian algebras in the bulk. This talk presents a lattice realization of this macroscopic mathematical description based on Kitaev's quantum double models. We demonstrate how category-theoretic axioms of Lagrangian algebras generate explicit operator consistency equations in the lattice Hilbert space. Solutions to these equations reproduce Lagrangian algebra classifications under specific conditions. Some representative concrete examples will be provided. Based on joint work with Xiao-Han Yang and Xiao-Yu Dong (arXiv:2504.19512).