Topological invariance and global Berry phase in non-Hermitian systems

被引:200
作者
Liang, Shi-Dong [1 ]
Huang, Guang-Yao
机构
[1] Sun Yat Sen Univ, State Key Lab Optoelect Mat & Technol, Guangzhou 510275, Guangdong, Peoples R China
来源
PHYSICAL REVIEW A | 2013年 / 87卷 / 01期
关键词
QUANTUM; SPINTRONICS;
D O I
10.1103/PhysRevA.87.012118
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
By studying the topological invariance and Berry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance for non-Hermitian systems. We find that Q can identify topological invariance in two kinds of non-Hermitian model, the two-level non-Hermitian Hamiltonian and the bipartite dissipative model. For the bipartite dissipative model, an abrupt change of the Berry phase in the parameter space reveals a quantum phase transition and is related to the exceptional points. These results give the basic relationships between the Berry phase and the quantum and topological phase transitions of non-Hermitian systems. DOI: 10.1103/PhysRevA.87.012118
引用
收藏
页数:6
相关论文
共 41 条
[1]  
Bohm A., 2003, TEXT MONOGR
[2]   Scattering approach to parametric pumping [J].
Brouwer, PW .
PHYSICAL REVIEW B, 1998, 58 (16) :10135-10138
[3]   Geometric phase in open systems [J].
Carollo, A ;
Fuentes-Guridi, I ;
Santos, MF ;
Vedral, V .
PHYSICAL REVIEW LETTERS, 2003, 90 (16)
[4]   Geometric phases and criticality in spin-chain systems [J].
Carollo, ACM ;
Pachos, JK .
PHYSICAL REVIEW LETTERS, 2005, 95 (15)
[5]   GEOMETRICAL PHASE IN THE CYCLIC EVOLUTION OF NON-HERMITIAN SYSTEMS [J].
DATTOLI, G ;
MIGNANI, R ;
TORRE, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (24) :5795-5806
[6]   COMPLEX GEOMETRICAL PHASES FOR DISSIPATIVE SYSTEMS [J].
GARRISON, JC ;
WRIGHT, EM .
PHYSICS LETTERS A, 1988, 128 (3-4) :177-181
[7]   Berry phase and spin quantum Hall effect in the vortex state of superfluid 3He in two dimensions -: art. no. 174503 [J].
Goryo, J ;
Kohmoto, M .
PHYSICAL REVIEW B, 2002, 66 (17) :1-6
[8]  
Goryo J, 2002, PHYS REV B, V66, DOI 10.1103/PhysRevB.66.085118
[9]   Berry curvature on the Fermi surface: Anomalous Hall effect as a topological Fermi-liquid property [J].
Haldane, FDM .
PHYSICAL REVIEW LETTERS, 2004, 93 (20) :206602-1
[10]   Characterization of topological insulators: Chern numbers for ground state multiplet [J].
Hatsugai, Y .
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2005, 74 (05) :1374-1377