标题： 孤子的分数汤普森泵浦：非线性特征值问题的体-边对应的独特表现 显示英文标题

标题： Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems

摘要： 最近的基础研究利用辅助特征值$\hat{H}\Psi=\omega S(\omega)\Psi$建立了非线性特征值问题的体边对应关系，涵盖了线性 [T. Isobe 等，Phys. Rev. Lett. 132, 126601 (2024)] 和非线性 [Chenxi Bai 和 Zhaoxin Liang, Phys. Rev. A. 111, 042201 (2025)] 哈密顿量。这引发了一个基本问题：特征值非线性是否能产生传统方法中不存在的可观测物理现象 ($\hat{H}\Psi=E\Psi$)？在本工作中，我们展示了这种对应关系的第一个独特非线性表现：孤子的分数 Thouless 输运。通过对具有次近邻 (NNN) 耦合的扩展 Rice-Mele 模型中的非线性 Thouless 输运进行系统研究，我们发现 NNN 参数即使在传统方法中来自量化拓扑不变量的情况下，也能诱导分数拓扑相位。关键的是，这些分数相位在辅助特征值框架内得到了解释，将非线性谱特性直接与体边对应关系联系起来。这项工作揭示了非线性与 NNN 耦合相互作用产生的新现象，为设计拓扑绝缘体和在非线性区域控制量子边界态提供了关键见解。 显示英文摘要

摘要： Recent foundational studies have established the bulk-edge correspondence for nonlinear eigenvalue problems using auxiliary eigenvalues $\hat{H}\Psi=\omega S(\omega)\Psi$, spanning both linear [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024)] and nonlinear [Chenxi Bai and Zhaoxin Liang, Phys. Rev. A. 111, 042201 (2025)] Hamiltionians. This raises a fundamental question: Can eigenvalue nonlinearity generate observable physical phenomena absent in conventional approaches ($\hat{H}\Psi=E\Psi$)? In this work, we demonstrate the first uniquely nonlinear manifestation of this correspondence: fractional Thouless pumping of solitons. Through systematic investigation of nonlinear Thouless pumping in an extended Rice-Mele model with next-nearest-neighbor (NNN) couplings, we discover that the NNN parameters can induce fractional topological phases despite quantized topological invariants from conventional approaches. Crucially, these fractional phases are explained within the auxiliary eigenvalue framework, linking nonlinear spectral features directly to bulk-boundary correspondence. This work reveals novel phenomena emerging from the interplay between nonlinearity and NNN couplings, providing key insights for designing topological insulators and controlling quantum edge states in nonlinear regimes.