Exactly Solvable Points and Symmetry Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
Exactly Solvable Points and Symmetry Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
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锯齿形晶格上量子自旋的精确可解点和对称性保护拓扑相
DOI：
10.1103/physrevlett.122.180401
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发表时间：
2019
影响因子：
8.6
通讯作者：
Liu W Vincent
中科院分区：
文献类型：
--
作者：
Zou Haiyuan;Zhao Erhai;Guan Xi-Wen;Liu W Vincent
在一维强相互作用体系中，存在大量的保序拓扑相。然而，实现这些SPT阶段通常需要实验上难以达到的微调。而解析解的缺乏阻碍了对它们的多体波函数的理解。在这里，我们表明，两种SPT阶段自然产生的超冷极性分子限制在一个曲折的光学晶格。这个系统，最近的实验的动机，描述了一个自旋模型，其交换耦合可以通过外部场调谐，以达到之前没有研究过的自旋链或梯子的参数区域。在扩大的参数空间内，我们发现对于这两个相，基态波函数可以分别精确地沿沿着和在一个特殊点上得到。这些精确解为SPT相位及其边缘激发提供了清晰的物理图像。我们进一步得到的相图，通过使用无限时间演化块抽取和讨论的两个SPT阶段之间的相变和他们的实验签名。
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interactingsystems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases, respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.