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ZNBerry Phases in Symmetry Protected Topological Phases
Physical Review Letters ( IF 8.6 ) Pub Date : 2018-06-15 , DOI: 10.1103/physrevlett.120.247202
Toshikaze Kariyado , Takahiro Morimoto , Yasuhiro Hatsugai

We show that the ZN Berry phase (Berry phase quantized into 2π/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small system size. The ZN Berry phase is defined in a N1-dimensional parameter space of local gauge twists, which we call the “synthetic Brillouin zone,” and an appropriate choice of an integration path consistent with the symmetry of the system ensures exact quantization of the Berry phase. We demonstrate the usefulness of the ZN Berry phase by studying two 1D models of bosons, SU(3) and SU(4) Affleck-Kennedy-Lieb-Tasaki models, where topological phase transitions are captured by Z3 and Z4 Berry phases, respectively. We find that the exact quantization of the ZN Berry phase at the topological transitions arises from a gapless band structure (e.g., Dirac cones or nodal lines) in the synthetic Brillouin zone.

中文翻译:

对称受保护拓扑阶段中的ZNBerry阶段

我们表明 žñ 浆果阶段(浆果阶段量化为 2个π/ñ)提供了一个有用的工具,可以通过相关性较小的数值直接计算出具有相关性的对称受保护拓扑阶段的特征。这žñ 浆果阶段定义在 ñ-1个当地计曲折,我们称之为的维参数空间“合成布里渊区”,并整合路径与系统的对称一致的适当选择保证了贝里相位的精确量化。我们证明了žñ 通过研究玻色子的两个一维模型SU(3)和SU(4)Affleck-Kennedy-Lieb-Tasaki模型来研究Berry相,其中拓扑相变被捕获 ž3ž4浆果阶段分别。我们发现žñ 拓扑过渡处的浆果相来自合成布里渊区中的无隙带结构(例如,狄拉克锥或节点线)。
更新日期:2018-06-15
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