Isobe Takuma, Yoshida Tsuneya, Hatsugai Yasuhiro
Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan.
Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev Lett. 2024 Mar 22;132(12):126601. doi: 10.1103/PhysRevLett.132.126601.
Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.
尽管拓扑现象不仅在线性系统中，而且在非线性系统中都吸引了越来越多的关注，但到目前为止，尚未建立起本征值非线性情况下的体边对应关系。我们通过引入辅助本征值来解决这个问题。我们揭示，当非线性较弱但为有限值时（即辅助本征值对于物理本征值是单调的），辅助本征态的拓扑边缘态会拓扑性地继承为物理边缘态。这一结果导致了与本征值非线性相关的体边对应关系。
