量子霍尔电流对空间绝热微扰的线性响应
Purely linear response of the quantum Hall current to space-adiabatic perturbations
摘要：
使用最近开发的工具，从空间绝热微扰理论，特别是建设一个非平衡的几乎静止的状态，我们给出了一个新的证明，久保公式的霍尔电导率仍然有效，超出线性响应制度。特别是，我们证明了，在量子霍尔系统和陈氏绝缘体，横向响应电流量子化的感应电场的强度的任何顺序。后者被引入作为一个扰动的周期性的，频谱间隙平衡哈密顿通过一个线性潜在的;现有的证明的准确性久保公式依赖于时间依赖的磁势。该结果适用于模拟量子（反常）霍尔效应的连续和离散晶体系统。
英文摘要：
Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. In particular, we prove that, in quantum Hall systems and Chern insulators, the transverse response current is quantized up to any order in the strength of the inducing electric field. The latter is introduced as a perturbation to a periodic, spectrally gapped equilibrium Hamiltonian by means of a linear potential; existing proofs of the exactness of Kubo formula rely instead on a time-dependent magnetic potential. The result applies to both continuum and discrete crystalline systems modelling the quantum (anomalous) Hall effect.
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