论文标题
确切的移动性边缘，$ \ MATHCAL {PT} $ - 一维非速晶的对称性断裂和皮肤效应
Exact mobility edges, $\mathcal{PT}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
论文作者
论文摘要
我们提出了一种通用分析方法，以研究具有平等时间（$ \ Mathcal {pt} $）对称性的一维准晶体中的定位过渡，由复杂的Quasiperiodic Mosaic晶格模型描述。通过应用Avila的QuasiperiodicSchrödinger操作员的全球全球理论，我们获得了确切的移动性边缘，并证明了移动性边缘与$ \ Mathcal {pt} $ - 对称性破坏的边界相同，这也证明了扩展（本地化）状态和$ \ Mathcal Calcal {PT} $ {PT} $ {PT} $ - - （$ \ MATHCAL {pt} $ - 对称 - 破解）状态。此外，我们将这些模型推广到更通用的非重生跳跃的情况下，它破坏了$ \ Mathcal {pt} $对称性并通常会诱导皮肤效应，并获得迁移率边缘的一般和分析表达。虽然局部状态对边界条件不敏感，但是当周期性边界条件更改为开放边界条件时，扩展状态变为皮肤状态。这表明皮肤状态和局部状态可以与其边界共存由移动边缘确定。
We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($\mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avila's global theory of quasiperiodic Schrödinger operators, we obtain exact mobility edges and prove that the mobility edge is identical to the boundary of $\mathcal{PT}$-symmetry breaking, which also proves the existence of correspondence between extended (localized) states and $\mathcal{PT}$-symmetry ($\mathcal{PT}$-symmetry-broken) states. Furthermore, we generalize the models to more general cases with non-reciprocal hopping, which breaks $\mathcal{PT}$ symmetry and generally induces skin effect, and obtain a general and analytical expression of mobility edges. While the localized states are not sensitive to the boundary conditions, the extended states become skin states when the periodic boundary condition is changed to open boundary condition. This indicates that the skin states and localized states can coexist with their boundary determined by the mobility edges.
