Infinite family of three-dimensional Floquet topological paramagnets
Infinite family of three-dimensional Floquet topological paramagnets
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DOI：
10.1103/physrevb.97.245106
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发表时间：
2017-06
影响因子：
3.7
通讯作者：
A. Potter;A. Vishwanath;L. Fidkowski
中科院分区：
文献类型：
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作者：
A. Potter;A. Vishwanath;L. Fidkowski
在时间周期驱动系统中，我们发现了一个无限族的时间反转对称三维相互作用的玻色子或自旋拓扑绝缘体，我们称之为Floquet拓扑顺磁体（FTPMs）。这些FTPM相表现出在热平衡中不可能发生的内在动力学性质，并且由无限组$Z_2$值拓扑不变量控制，每个素数一个。拓扑不变量的物理特征是表面磁畴壁作为单向量子通道，在每个驱动周期内传输量子化的信息包。我们构建了实现这些阶段的精确可解模型，并讨论了它们的拓扑保护表面状态的异常动力学。与之前遇到的Floquet SPT相位的例子不同，这些三维ftpm不能通过群上同调方法捕获，并且不能通过简单地将离散时间平移作为普通对称来从平衡分类中获得。最简单的这种FTPM相位可以具有反常的$Z_2$（环码）表面拓扑顺序，其中每个Floquet周期交换规范电和磁激励，这在纯二维系统中不可能发生而不破坏时间反转对称性。
We uncover an infinite family of time-reversal symmetric 3d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium, and are governed by an infinite set of $Z_2$-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3d FTPMs are not captured by group cohomology methods, and cannot be obtained from equilibrium classifications simply by treating the discrete time-translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous $Z_2$ (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2d system without breaking time reversal symmetry.