论文标题

电化及其在一维非铁链中的量化

Electric polarization and its quantization in one-dimensional non-Hermitian chains

论文作者

Hu, Jinbing, Perroni, Carmine Antonio, De Filippis, Giulio, Zhuang, Songlin, Marrucci, Lorenzo, Cardano, Filippo

论文摘要

我们将现代的电极化理论推广到具有线路频谱的一维非速度系统的情况。在这些系统中,即使投影到能量差距以下状态的子空间时,电子位置运算符也是非热的。然而,相关的威尔逊环操作员在热力学极限上是生物三相统一的,从而导致了实价的电子位置,从而可以清晰地定义极化。对于遗传学绝缘子,可以在存在某些对称性的情况下进行量化非热的极化。然而,与后一种情况不同,在这种状态极化中,量化也取决于能量差距的类型,能量差距可以是真实的或虚构的,从而导致各种拓扑阶段。最违反直觉的例子是只有时间反向对称性的一维非链链,在存在假想的线间隙的情况下量化了非热偏极化。我们提出了两个特定模型,以提供支持我们发现的数值证据。

We generalize the modern theory of electric polarization to the case of one-dimensional non-Hermitian systems with line-gapped spectrum. In these systems, the electronic position operator is non-Hermitian even when projected into the subspace of states below the energy gap. However, the associated Wilson-loop operator is biorthogonally unitary in the thermodynamic limit, thereby leading to real-valued electronic positions that allow for a clean definition of polarization. Non-Hermitian polarization can be quantized in the presence of certain symmetries, as for Hermitian insulators. Different from the latter case, though, in this regime polarization quantization depends also on the type of energy gap, which can be either real or imaginary, leading to a richer variety of topological phases. The most counter-intuitive example is the 1D non-Hermitian chain with time-reversal symmetry only, where non-Hermitian polarization is quantized in presence of an imaginary line-gap. We propose two specific models to provide numerical evidence supporting our findings.

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