带隙相互作用晶格系统的Hall电导和磁通插入统计
Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
摘要：
研究了零温无限体积带隙二维短程相互作用晶格系统的电荷输运。我们表明，霍尔电导是本地可计算的，是相同的所有系统，这是在相同的间隙相位。我们提供了一个严格的版本的劳克林的磁通插入的论点，这表明，对于短程纠缠系统的霍尔电导是一个整数倍的e^2/h。我们表明，霍尔电导决定磁通插入的统计。对于玻色子短程纠缠系统，这意味着霍尔电导是e^2/h的偶数倍。最后，我们适应的情况下，在一维无限体积的带隙晶格系统的量子化的无源电荷泵的证明。
英文摘要：
We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems which are in the same gapped phase. We provide a rigorous versions of Laughlin's flux-insertion argument which shows that for short-range entangled systems the Hall conductance is an integer multiple of e^2/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e^2/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.
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