Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA.
Phys Rev Lett. 2019 Mar 22;122(11):118001. doi: 10.1103/PhysRevLett.122.118001.
Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example, for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of interline interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.
拓扑量子和经典材料可以表现出对无序具有鲁棒性的特性，例如对于非相互作用的粒子和线性波。在这里，我们展示了如何构建拓扑保护态，这些拓扑保护态源自于软物质或小型化机械结构固有的强相互作用和热涨落。具体来说，我们考虑了在张力下的波动线（例如聚合物或涡旋线），这些波动线受到一类空间调制基底势的影响。在平衡状态下，这些线会获得与整数拓扑不变量（称为陈数）成正比的集体倾斜。这种量子化的倾斜对基底无序具有鲁棒性，这一点通过经典 Langevin 动力学模拟得到了验证。这种鲁棒性源于系统中热涨落线的激发由于线间相互作用而被能隙隔开。我们通过开发的一种映射来建立这个体系的拓扑基础，该映射将相互作用线系统与 Thouless 泵浦到虚时间的一个迄今为止尚未被探索的广义进行了关联。我们的工作指出了一类新的经典拓扑现象，其中拓扑特征在有限温度下观察到的结构性质中表现出来，而不是在传输测量中表现出来。
