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Bipartite charge fluctuations in one-dimensional Z_2 superconductors and insulators

机译：一维Z_2超导体和绝缘子的双向电荷涨落

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摘要

Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional Z_2 (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the XYZ model.
机译：已经引入了二分电荷波动（BCF），以提供多体纠缠的实验指示。他们已经证明自己是表征各种量子模型中量子相变的非常有效和有用的工具，这些量子模型可保存粒子总数（或自旋系统的磁化强度），并且可以通过实验进行测量。我们在通用的一维Z_2（拓扑）模型中研究BCF，包括Kitaev超导线模型，伊辛链或各种拓扑绝缘体（例如Su-Schrieffer-Heeger模型）。所考虑的电荷（铁离子数或相对密度）不再守恒，从而导致粒子数的宏观波动。我们证明，在以线性弥散为特征的相变中，BCF探测了绕组数的变化，该变化使人可以查明过渡并对应于标准模型的拓扑不变式。此外，我们证明在精确的临界点上仍存在大量对数贡献。它的量化系数具有通用性，可表征关键模型。结果扩展到Rashba拓扑纳米线和XYZ模型。

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  • 来源
    《Physical review》 |2017年第12期|121113.1-121113.6|共6页
  • 作者

    Loiec Herviou; Christophe Mora; Karyn Le Hur;

  • 作者单位

    Centre de Physique Theorique, Ecole Polytechnique, CNRS, Universite Paris-Saclay, 91128 Palaiseau, France,Laboratoire Pierre Aigrain, Ecole Normale Supirieure-PSL Research University, CNRS, Universite Pierre et Marie Curie-Sorbonne University, Universite Paris Diderot-Sorbonne Paris Cite, 24 rue Lhomond, 75231 Paris Cedex 05, France;

    Laboratoire Pierre Aigrain, Ecole Normale Supirieure-PSL Research University, CNRS, Universite Pierre et Marie Curie-Sorbonne University, Universite Paris Diderot-Sorbonne Paris Cite, 24 rue Lhomond, 75231 Paris Cedex 05, France;

    Centre de Physique Theorique, Ecole Polytechnique, CNRS, Universite Paris-Saclay, 91128 Palaiseau, France;

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