Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
IBM Research, MIT-IBM A.I. Lab, 75 Binney Street, Cambridge, Massachusetts 02142, USA.
Phys Rev Lett. 2018 Sep 21;121(12):126803. doi: 10.1103/PhysRevLett.121.126803.
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.
在最近的实验中，时间相关的周期性场被用来创造具有潜在应用的奇异拓扑物质相，从量子输运到量子计算。在高驱动频率下，这些非平衡态表现出对局部无序的典型鲁棒性，类似于平衡拓扑相。然而，在一般情况下证明这些拓扑相的存在是一个开放的问题。我们提出了一个普遍的有效理论，利用现代自由概率理论和随机矩阵的思想，对有限驱动频率和一系列无序情况下拓扑相的存在进行了分析预测。我们发现，取决于无序的强度，这样的系统可能是拓扑的或平凡的，而且两者之间存在着转变。具体来说，该理论预测了两个相之间的转变的临界点，并提供了临界指数。我们通过将理论结果与驱动无序 1D Kitaev 链和 2D Bernevig-Hughes-Zhang 模型的精确对角化进行比较来验证我们的结果，发现吻合得很好。这封信可能会指导探索拓扑相的实验工作。
