Effect of disorder on topological charge pumping in the Rice-Mele model
Effect of disorder on topological charge pumping in the Rice-Mele model
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DOI：
10.1103/physreva.103.043310
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发表时间：
2020-10
影响因子：
2.9
通讯作者：
A. Hayward;E. Bertok;U. Schneider;F. Heidrich-Meisner
中科院分区：
文献类型：
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作者：
A. Hayward;E. Bertok;U. Schneider;F. Heidrich-Meisner
最近的超冷量子气体实验成功地实现了光学晶格中整数量子化的拓扑电荷泵浦。基于这一进展，我们研究了静态无序对拓扑索利斯电荷泵浦的影响。我们关注自由无自旋费米子的半填充Rice-Mele模型，并考虑随机对角无序。在瞬时基础上，我们计算了偏振、纠缠谱和局部陈氏标记。作为第一个主要结果，我们得出结论，空间集成局部陈氏标记最适合于无序系统中拓扑转换的定量确定。在时间相关的模拟中，我们使用时间积分电流来获得慢周期驱动系统中的泵浦电荷。作为第二个主要结果，我们观察和表征了量子化电荷泵的无序驱动击穿。计算泵浦电荷的静态方法和随时间变化的方法之间有很好的一致性。拓扑跃迁很好地发生在所有状态都在给定系统大小上局域化的状态下，因此与哈密顿特征态的离域-局域跃迁无关。对于单个失序实现，当从洁净系统的带隙继承的谱体间隙闭合时，参数的量子化抽运发生击穿，导致全局无间隙谱。作为第三个主要结果，关于有限尺寸系统的分析，我们表明体积间隙的无序平均严重高估了量化泵浦的稳定性。一个更好的估计是能量间隙分布的典型值，也称为分布模式。
Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.