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Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
Journal of Mathematical Physics ( IF 1.3 ) Pub Date : 2020-10-01 , DOI: 10.1063/5.0022944
Anton Kapustin 1 , Nikita Sopenko 1
Affiliation  

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 that are in the same gapped phase. We provide a rigorous version of Laughlin’s flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e2/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 e2/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.

中文翻译:

霍尔电导和有隙相互作用晶格系统中通量插入的统计

我们研究了具有短程相互作用的二维零温度无限体积有隙晶格系统的电荷传输。我们表明霍尔电导是局部可计算的,并且对于处于相同间隙相位的所有系统都是相同的。我们提供了劳克林通量插入论证的严格版本,它表明对于短程纠缠系统,霍尔电导是 e2/h 的整数倍。我们表明霍尔电导决定了通量插入的统计数据。对于玻色子短程纠缠系统,这意味着霍尔电导是 e2/h 的偶数倍。最后,我们将 Thouless 电荷泵的量化证明应用于一维无限体积有隙晶格系统的情况。
更新日期:2020-10-01
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