标题： 拓扑能带对晶格势和杂质的鲁棒平移不变性 显示英文标题

标题： Robust translational invariance in topological bands against lattice potentials and disorders

摘要： 我们从理论上证明，单个Landau能级(LL)的Hilbert(子)空间内的连续磁性平移不变性即使在存在超晶格静电势调制的情况下也能持续存在，而在整个实空间Hilbert空间中这种不变性会被破坏。 这是由于超晶格常数与量子霍尔流体的基本长度尺度之间的相互作用。 特别是对于最低的LL（LLL），当超晶格间距小于磁长度时，连续的磁性平移对称性非常稳健。 对于分数量子霍尔相，当超晶格间距小于我们现在已经可以定量定义的相应基本长度时，连续的平移对称性得以保持，这与来自量子度量的长度尺度不同。 此外，我们的分析表明，任意子激发的动力学可以对无序的长波部分具有鲁棒性，并且我们讨论了相关的实验影响。 显示英文摘要

摘要： We theoretically show that the continuous magnetic translational invariance within the Hilbert (sub-)space of a single Landau level (LL) can persist even in the presence of a superlattice electrostatic potential modulation, while such invariance is broken in the full real-space Hilbert space. This is due to the interplay of the superlattice constant and the fundamental length scale of the quantum Hall fluids. In particular for the lowest LL (LLL), when the spacing of superlattice is below the magnetic length, continuous magnetic translational symmetry is very robust. For the fractional quantum Hall phases, the continuous translational symmetry is preserved when the superlattice spacing is below the corresponding fundamental lengths which we can now quantitatively define, which is different from the length scale from the quantum metric. Moreover, our analysis implies that the dynamics of the anyonic excitations can be robust against the long wavelength part of the disorder, and we discuss the related experimental ramifications.