ZN Berry Phases in Symmetry Protected Topological Phases
ZN Berry Phases in Symmetry Protected Topological Phases
复制标题
DOI：
10.1103/physrevlett.120.247202
复制
发表时间：
2018-06-15
影响因子：
8.6
通讯作者：
Hatsugai, Yasuhiro
中科院分区：
文献类型：
--
作者：
Kariyado, Toshikaze;Morimoto, Takahiro;Hatsugai, Yasuhiro
我们表明，Z（N）Berry相位（Berry相位量化为2 π/N）提供了一个有用的工具来表征对称性保护的拓扑相位与相关性，可以直接计算通过一个相对较小的系统大小的数值。Z（N）Berry相定义在N - 1维的局部规范扭曲的参数空间中，我们称之为“合成布里渊区”，并且适当选择与系统对称性一致的积分路径确保了Beny相的精确量子化。我们通过研究两个一维玻色子模型SU（3）和SU（4）Aftleck-Kennedy-Lieb-Tasaki模型，证明了Z（N）Berry相的有效性，其中拓扑相变分别被Z（3）和Z（4）Berry相捕获.我们发现，Z（N）Berry相位在拓扑跃迁处的精确量子化源于无隙能带结构（例如，狄拉克锥或节线）在合成布里渊区。
We show that the Z(N) Berry phase (Berry phase quantized into 2 pi/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can he directly computed through numerics of a relatively small system size. The Z(N) Berry phase is defined in a N - 1-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 Beny phase. We demonstrate the usefulness of the Z(N) Berry phase by studying two 1D models of bosons, SU(3) and SU(4) Aftleck-Kennedy-Lieb-Tasaki models, where topological phase transitions are captured by Z(3) and Z(4) Berry phases, respectively. We find that the exact quantization of the Z(N) Berry phase at the topological transitions arises from a gapless band structure (e.g., Dirac cones or nodal lines) in the synthetic Brillouin zone.