环面上相互作用电子霍尔电导的量子化
Quantization of Hall Conductance For Interacting Electrons on a Torus
摘要：
我们考虑相互作用，带电荷的自旋环面所描述的一个缺口的哈密顿与一个独特的基态和保守的本地电荷。利用基态在磁通环周围的准绝热演化，我们证明了，在没有任何平均假设的情况下，基态的霍尔电导是以e^2/h的整数倍量子化的，直到系统线性尺寸的指数小修正。此外，我们讨论了分数量子化的情况下，一个额外的拓扑顺序假设的退化基态子空间的扩展。
英文摘要：
We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e^2/h, up to exponentially small corrections in the linear size of the system. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.
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