Date:2012-01-13, 10:00am

Venue:Conference Hall 213, Science Building

Title: Boundary excitations of Levin-Wen Model

Speaker: Lan Tian

Department of Physics, Tsinghua

Abstract:I will introduce the Levin-Wen Model with a boundary line. In the bulk of LW model, local unitary transformations, such as F-move, will lead to the mathematical structure called tensor category. We require that the boundary admit similar local transformations, which are compatible with bulk ones (The boundary has module category structure under this requirement.) Then I will study the excitations on the boundary. The approach is to study the surrounding area of a boundary excitation. We find the area can be divided into two parts: one stands for local operator algebras; the other stands for modules, or representations, over these algebras, and the excitation sits in the ``module" part. Then we can classify the boundary excitation by studying the algebra representations. This is similar to classifying particles by group representations. I will give examples of the approach in some simple cases, such as in the toric code model.