一维长程非互易晶格中谱拓扑的演化
Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
摘要：
我们研究了一维格点的谱拓扑，其中最近的$r_d$相邻点之间的非互易跳跃是相同的。对于纯非对角模型没有现场电位，周期性边界条件（PBCs）下的晶格的能谱形成一个不可分割的环，与自己在复杂的能量平面交织，其特征在于从1到$r_d$的缠绕数。开边界条件下的相应谱在最近邻模型中是实数，它将分叉并形成一个$(r_d+1)$ -指向的星形，所有分支都以零能量连接。如果我们进一步引入周期性的现场调制，随着我们改变参数，频谱将逐渐分成多个可分离的频带。最重要的是，我们发现在PBC光谱中可以存在一种不同类型的带隙，称为环隙，将内环与外环分开，每个环由光谱的一部分组成。此外，具有现场电位的体系的OBC谱中也存在环结构。我们进一步研究了具有幂律衰减的长程非互易跳跃的晶格，发现PBC谱中的纠缠环将被解开。最后，我们提出了一个实验方案，实现远程非互易模型，利用电路。我们的工作揭示了长程非互易晶格中奇异的谱拓扑。
英文摘要：
We investigate the spectral topology of one-dimensional lattices where the nonreciprocal hoppings within the nearest $r_d$ neighboring sites are the same. For the purely off-diagonal model without onsite potentials, the energy spectrum of the lattice under periodic boundary conditions (PBCs) forms an inseparable loop that intertwines with itself in the complex energy plane and is characterized by winding numbers ranging from 1 up to $r_d$. The corresponding spectrum under open boundary conditions (OBCs), which is real in the nearest neighboring model, will ramify and take the shape of an $(r_d+1)$-pointed star with all the branches connected at zero energy. If we further introduce periodic onsite modulations, the spectrum will gradually divide into multiple separable bands as we vary the parameters. Most importantly, we find that a different kind of band gap called loop gap can exist in the PBC spectrum, separating an inner loop from an outer one with each composed by part of the spectrum. In addition, loop structures also exist in the OBC spectra of systems with onsite potentials. We further study the lattices with power-law decaying long-range nonreciprocal hopping and found that the intertwined loops in the PBC spectrum will be untangled. Finally, we propose an experimental scheme to realize the long-range nonreciprocal models by exploiting electrical circuits. Our work unveils the exotic spectral topology in the long-range nonreciprocal lattices.
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