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Yu, Yue; Yu, Y , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China
Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds
Source PublicationNUCLEAR PHYSICS B
KeywordQuantum Hall States Riemannian Geometry Spectral Asymmetry Elliptic Operators Field-theory Edge Excitations Boundary Conductance Dimensions Invariant
AbstractWe construct an exactly soluble spin-model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2 + 1 dimensions. (c) 2008 Elsevier B.V. All rights reserved.
2008
ISSN0550-3213
Volume799Issue:3Pages:345-363
Subject AreaPhysics
Indexed BySCI
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Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/5479
Collection理论物理所科研产出_SCI论文
Corresponding AuthorYu, Y , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Yu, Yue,Yu, Y , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China. Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds[J]. NUCLEAR PHYSICS B,2008,799(3):345-363.
APA Yu, Yue,&Yu, Y , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.(2008).Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds.NUCLEAR PHYSICS B,799(3),345-363.
MLA Yu, Yue,et al."Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds".NUCLEAR PHYSICS B 799.3(2008):345-363.
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