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

TL;DR

This paper demonstrates a novel nonlinear phenomenon called fractional Thouless pumping of solitons, revealing how eigenvalue nonlinearity can produce observable effects like fractional topological phases in a nonlinear extended Rice-Mele model.

Contribution

It introduces the first observation of fractional Thouless pumping in a nonlinear setting, linking nonlinear spectral properties to bulk-edge correspondence via auxiliary eigenvalues.

Findings

Fractional topological phases induced by NNN couplings.

Nonlinear spectral characteristics explain fractional pumping.

Emergent phenomena from nonlinearity and NNN interactions.

Abstract

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 progress prompts a fundamental question: Can eigenvalue nonlinearity generate observable physical phenomena absent in conventional approaches ($\hat{H}\Psi=E\Psi$)? In this work, we address this question by demonstrating the first uniquely nonlinear manifestation of the bulk-edge correspondence: fractional Thouless pumping of solitons. Through systematic investigation of nonlinear Thouless pumping in an extended Rice-Mele model incorporating next-nearest-neighbor (NNN) couplings, we uncover that NNN interaction parameters can induce fractional topological phases|even in the presence of quantized topological invariants as predicted by conventional linear approaches. Crucially, these fractional phases are naturally explained within the auxiliary eigenvalue framework, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and NNN couplings, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in nonlinear regimes.