Topological phase transition on the edge of two-dimensional Z(2) topological order

Chen, Wei-Qiang1,2,3; Jian, Chao-Ming4; Kong, Liang2,5,7; You, Yi-Zhuang6; Zheng, Hao2,5,7,8

2020-07-23

10.1103/PhysRevB.102.045139

PHYSICAL REVIEW B   影响因子和分区

2469-9950

2469-9969

The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d Z(2) topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d Z(2) topological order. Then, we use an explicit lattice model construction to realize a topological phase transition between the two well-known gapped edges of the 2d Z(2) topological order, and show that all the ingredients of the above enriched fusion category can be realized explicitly in this lattice model.

SCI ; EI

英语

第一 ; 通讯

National Key Research and Development Program of China[2016YFA0300300] ; NSFC[11674151][11861161001][11971219][11871078][11131008] ; Gordon and Betty Moore Foundations EPiQS Initiative[GBMF4304] ; Science, Technology and Innovation Commission of Shenzhen Municipality[ZDSYS20170303165926217] ; Guangdong Provincial Key Laboratory[2019B121203002]

Materials Science ; Physics

Materials Science, Multidisciplinary ; Physics, Applied ; Physics, Condensed Matter

WOS:000551341900004

AMER PHYSICAL SOC

20204309389117

Crystal lattices

Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4 ; Crystal Lattice:933.1.1

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Shenzhen Key Lab Adv Quantum Funct Mat & Devices, Shenzhen 518055, Peoples R China
4.Univ Calif Santa Barbara, Kavli Inst Theoret Phys, Santa Barbara, CA 93106 USA
5.Southern Univ Sci & Technol, Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
6.Univ Calif San Diego, Dept Phys, La Jolla, CA 92093 USA
7.Southern Univ Sci & Technol, Shenzhen Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Peking Univ, Dept Math, Beijing 100871, Peoples R China

Chen, Wei-Qiang,Jian, Chao-Ming,Kong, Liang,et al. Topological phase transition on the edge of two-dimensional Z(2) topological order[J]. PHYSICAL REVIEW B,2020,102(4).

Chen, Wei-Qiang,Jian, Chao-Ming,Kong, Liang,You, Yi-Zhuang,&Zheng, Hao.(2020).Topological phase transition on the edge of two-dimensional Z(2) topological order.PHYSICAL REVIEW B,102(4).

Chen, Wei-Qiang,et al."Topological phase transition on the edge of two-dimensional Z(2) topological order".PHYSICAL REVIEW B 102.4(2020).