论文标题
一维远程非核心晶格中光谱拓扑的演变
Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
论文作者
论文摘要
我们研究了一维晶格的频谱拓扑，其中最接近$ r_d $邻居站点内的非重新射击跳跃是相同的。对于没有现场电势的纯粹的非对角线模型，在周期性边界条件（PBCS）下晶格的能量谱形成一个不可分割的环路，该环路与自身在复杂的能量平面中交织在一起，其特征是绕线数范围从1到$ r_d $。在最近的相邻模型中是真实的开放边界条件（OBC）下的相应光谱，将分析并采用$（r_d+1）$尖的恒星的形状，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，则随着我们改变参数，频谱将逐渐分为多个可分离的频段。最重要的是，我们发现PBC频谱中可以存在一种不同类型的称为环间隙的带隙，将内部环与外部环分开，每个环由频谱的一部分组成。此外，具有现场电势的系统的OBC光谱中也存在循环结构。我们进一步研究了用幂律衰减的远程非重点跳跃的晶格，发现PBC频谱中的相互交织环将没有弄清。最后，我们提出了一个实验方案，通过利用电路来实现远程非偏置模型。我们的工作揭示了在远程非注射晶格中的外来频谱拓扑结构。
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.
