Stability of Periodically Driven Topological Phases against Disorder.
Stability of Periodically Driven Topological Phases against Disorder.
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DOI：
10.1103/physrevlett.121.126803
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发表时间：
2018-03
影响因子：
8.6
通讯作者：
O. Shtanko;R. Movassagh
中科院分区：
文献类型：
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作者：
O. Shtanko;R. Movassagh
在最近的实验中，依赖于时间的周期性场被用来创建具有从量子传输到量子计算的潜在应用的物质的奇异拓扑相。这些非平衡态，在高的驱动频率，表现出典型的鲁棒性，对当地的混乱类似的平衡拓扑相位。然而，证明存在这样的拓扑相位在一般设置是一个开放的问题。我们提出了一个通用的有效理论，利用现代自由概率理论和随机矩阵的思想，分析预测有限的驱动频率和范围内的混乱的拓扑相位的存在。我们发现，根据无序的强度，这样的系统可能是拓扑的或平凡的，并且在两者之间存在过渡。特别地，该理论预测了两个相之间的过渡的临界点，并提供了临界指数。我们证实了我们的结果，通过比较它们的驱动无序的一维Kitaev链和二维Bernevig-Hughes-Zhang模型的精确对角化，并找到很好的协议。这封信可以指导探索拓扑相的实验工作。
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.