Topological Phase Transition of Non‐Hermitian Crosslinked Chain,Annalen Der Physik

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Topological Phase Transition of Non‐Hermitian Crosslinked Chain
Annalen Der Physik ( IF 2.2 ) Pub Date : 2020-04-29 , DOI: 10.1002/andp.201900402
X. L. Zhao _{1,

2} , L. B. Chen ₂ , L. B. Fu ₁ , X. X. Yi ₃

Affiliation

The contents of topological classification of matter are enriched by non‐Hermiticity, such as exceptional points, bulk‐edge correspondence, and skin effects. Physically, gain and loss can be introduced by imaginary on‐site potentials of lattice Hamiltonians, and the topological phase transition for a cross‐linked chain in the presence of such non‐Hermiticity is investigated. The topological phase diagram in terms of a winding number is obtained analytically with phase boundaries coinciding with the surfaces of exceptional points. The topologically original edge states with distribution mainly at the joints between domains of different phases are protected even for long chains. The non‐Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies, expected values of Pauli matrices, and trajectories of these quantities. This model may be implemented in coupled photonic crystals, fermions trapped in optical lattice, or non‐Hermitian electrical‐circuit lattices, and the edge states are immune to various kinds of disorders until topological phase transition occurs. This work gives insight into the influence of non‐Hermiticity on topological phase of matter.

中文翻译：

非埃尔米特交联链的拓扑相变

物质的拓扑分类的内容因非稀疏性而得以丰富，例如例外点，块边对应关系和集肤效应。从物理上讲，可以通过想象中的汉密尔顿点阵势来引入增益和损耗，并研究存在这种非赫米替性的交联链的拓扑相变。以绕组数为单位的拓扑相位图是通过解析获得相位边界与例外点表面一致的拓扑图。甚至在长链中，主要在不同相域之间的接头处分布的拓扑原始边缘状态也受到保护。非赫米特拓扑特征也可以通过复杂本征能矢量场中的涡旋结构，保利矩阵的期望值，和这些量的轨迹。该模型可以在耦合的光子晶体，陷在光学晶格中的费米子或非厄密电路的晶格中实现，并且边缘状态可以抵抗各种紊乱，直到发生拓扑相变为止。这项工作可以洞悉非赫米性对物质拓扑阶段的影响。

更新日期：2020-04-29

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