Twisted Quantum Double Model of Topological Orders with Boundaries

admin   2020-01-06 18:40:32   2734

报告题目:Twisted Quantum Double Model of Topological Orders with Boundaries
报告时间:2020-01-07 09:30 (星期二)
报告地点:北洋园校区理学院32教256
报告人:万义顿教授( 复旦大学)

报告摘要: 

We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group G and a 3-cocycle in the third cohomology group of G over U (1), a boundary Hamiltonian can be defined by a subgroup K of G and a 2-cochain in the second cochain group of K over U (1). The consistency between the bulk and boundary Hamiltonians is dictated by what we call the Frobenius condition that constrains the 2-cochain given the 3-cocyle. We offer a closed-form formula computing the ground-state degeneracy of the model on a cylinder in terms of the input data only, which can be naturally generalized to surfaces with more boundaries. We also explicitly write down the ground-state wave function of the model on a disk also in terms of the input data only. 


报告人简介: 

万义顿:男,复旦大学物理系教授,华南理工大学计算机与经济学双学士(1998)、美国宾夕法尼亚大学计算机硕士(2002)、加拿大渥太华大学物理硕士(2004)、加拿大滑铁卢大学暨圆周理论物理研究所理论物理博士(2009),于日本近畿大学、东京大学、加拿大圆周理论物理研究所做博士后,2016年加入复旦物理系,从事拓扑物态、量子信息与计算、量子引力等领域的交叉研究。


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