From effective Hamiltonian to anomaly inflow in topological orders with boundaries

Hu, Yuting1,2,3; Wan, Yidun1,2,3,4,5,6,7; Wu, Yong-Shi1,2,3,4,8

2018-08-16

10.1007/JHEP08(2018)092

JOURNAL OF HIGH ENERGY PHYSICS   影响因子和分区

1029-8479

Whether two boundary conditions of a two-dimensional topological order can be continuously connected without a phase transition in between remains a challenging question. We tackle this challenge by constructing an effective Hamiltonian of anyon interaction that realizes such a continuous deformation. At any point along the deformation, the model remains a fixed point model describing a gapped topological order with gapped boundaries. That the deformation retains the gap is due to the anomaly cancelation between the boundary and bulk. Such anomaly inflow is quantitatively studied using our effective Hamiltonian. We apply our method of effective Hamiltonian to the extended twisted quantum double model with boundaries (constructed by two of us in ref. [1]). We show that for a given gauge group G and a three-cocycle in H-3[G, U(1)] in the bulk, any two gapped boundaries for a fixed subgroup K subset of G on the boundary can be continuously connected via an effective Hamiltonian. Our results can be straightforwardly generalized to the extended Levin-Wen model with boundaries (constructed by three of us in ref. [2]).

Anomalies in Field and String Theories Anyons Topological Field Theories Topological States of Matter

SCI

英语

NI论文

通讯

Shanghai Pujiang Program[KBH1512328]

Physics

Physics, Particles & Fields

WOS:000441810000003

SPRINGER

PHYSICS

Web of Science

1.Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China
2.Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China
3.Fudan Univ, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China
4.Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Jiangsu, Peoples R China
5.Fudan Univ, Inst Nanoelect Devices & Quantum Comp, Shanghai 200433, Peoples R China
6.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
7.Southern Univ Sci & Technol, Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Univ Utah, Dept Phys & Astron, Salt Lake City, UT 84112 USA

Hu, Yuting,Wan, Yidun,Wu, Yong-Shi. From effective Hamiltonian to anomaly inflow in topological orders with boundaries[J]. JOURNAL OF HIGH ENERGY PHYSICS,2018(8).

Hu, Yuting,Wan, Yidun,&Wu, Yong-Shi.(2018).From effective Hamiltonian to anomaly inflow in topological orders with boundaries.JOURNAL OF HIGH ENERGY PHYSICS(8).

Hu, Yuting,et al."From effective Hamiltonian to anomaly inflow in topological orders with boundaries".JOURNAL OF HIGH ENERGY PHYSICS .8(2018).