涨落虚规范场中的拓扑相变
Topological phase transition in fluctuating imaginary gauge fields
AI总结：
本文通过虚规范变换将具有空间涨落虚规范场的非厄米晶格映射为谱等价的周期晶格，解析预测了键无序非周期晶格的拓扑不变性和边界局域化，并在准周期规范场中发现由场强控制的拓扑相变。
摘要：
我们研究了非厄米晶格模型中的精确可解性和点隙拓扑相变。这些模型包含依赖于格点的非互易跃迁 $J e^{\pm g_n}$，这种跃迁由空间涨落的虚规范场 $ig_n \hat~x$ 促成，该规范场破坏了平移对称性。通过采用适当的虚规范变换，研究表明：在开放边界条件下，任意给定 $g_n$ 的晶格在谱上等价于一个无场的晶格。此外，具有闭合边界的系统可以简化为一个谱等价的晶格，该晶格具有均匀的平均场 $i\bar{g}\hat~x$。该框架为解析预测键无序非周期晶格的谱拓扑不变性及相关的边界局域化现象提供了一种全面的方法。这些预测通过分析规范变换后的等谱周期晶格来实现。值得注意的是，对于具有准周期 $g_n= \ln |λ\cos 2παn|$ 和无理数 $α$ 的晶格，揭示了一个此前未知的拓扑相变。观察到拓扑谱指标 $W$ 取值为 $-N$ 或 $+N$，导致所有 $N$ 个开放边界本征态要么局域在右边缘，要么局域在左边缘，这仅取决于规范场的强度，即 $λ<2$ 或 $λ>2$。在临界点 $λ\approx2$ 处识别出一个相变，此时所有本征态都发生退局域化。该理论已被证明适用于长程跃迁模型和更高维度。
英文摘要：
We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\pm g_n}$, facilitated by a spatially fluctuating imaginary gauge field $ig_n \hat~x$ that disrupts translational symmetry. By employing suitable imaginary gauge transformations, it is revealed that a lattice characterized by any given $g_n$ is spectrally equivalent to a lattice devoid of fields, under open boundary conditions. Furthermore, a system with closed boundaries can be simplified to a spectrally equivalent lattice featuring a uniform mean field $i\bar{g}\hat~x$. This framework offers a comprehensive method for analytically predicting spectral topological invariance and associated boundary localization phenomena for bond-disordered nonperiodic lattices. These predictions are made by analyzing gauge-transformed isospectral periodic lattices. Notably, for a lattice with quasiperiodic $g_n= \ln |λ\cos 2παn|$ and an irrational $α$, a previously unknown topological phase transition is unveiled. It is observed that the topological spectral index $W$ assumes values of $-N$ or $+N$, leading to all $N$ open-boundary eigenstates localizing either at the right or left edge, solely dependent on the strength of the gauge field, where $λ<2$ or $λ>2$. A phase transition is identified at the critical point $λ\approx2$, at which all eigenstates undergo delocalization. The theory has been shown to be relevant for long-range hopping models and for higher dimensions.
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