2015年4月
Symmetry-protected topological order in magnetization plateau states of quantum spin chains
PHYSICAL REVIEW B
- ,
- ,
- 巻
- 91
- 号
- 15
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevB.91.155136
- 出版者・発行元
- AMER PHYSICAL SOC
A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization plateau states of one-dimensional antiferromagnets which satisfy the conditions S - m is an element of odd integer, where S is the spin quantum number and m the magnetization per site, can be identified as symmetry-protected topological states if an inversion symmetry about the link center is present. This assertion is reached by mapping the antiferromagnet into a nonlinear sigma model type effective field theory containing a novel Berry phase term (a total derivative term) with a coefficient proportional to the quantity S - m, and then analyzing the topological structure of the ground state wave functional which is inherited from the latter term. A boson-vortex duality transformation is employed to examine the topological stability of the ground state in the absence/presence of a perturbation violating link-center inversion symmetry. Our prediction based on field theories is verified by means of a numerical study of the entanglement spectra of actual spin chains, which we find to exhibit twofold degeneracies when the aforementioned condition is met. We complete this study with a rigorous analysis using matrix product states.
- リンク情報
- ID情報
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- DOI : 10.1103/PhysRevB.91.155136
- ISSN : 1098-0121
- eISSN : 1550-235X
- Web of Science ID : WOS:000353283800001