Nonreciprocity Induced Fractional Nonlinear Thouless Pumping

Abstract

Recent interest has surged in eigenvalue's nonlinearity-based topological transport governed by the equation of auxiliary eigenvalues $H\Psi =\omega S(\omega )\Psi$ [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024); C. Bai and Z. Liang, 111, 042201 (2025); Phys. Rev. A 112, 052207 (2025)] rather than the conventional Schrodinger equation $H\Psi =E\Psi$ in conservative settings, yet non-Hermitian generalizations remain uncharted. In this work, we are motivated to investigate the nonlinear Thouless pumping in a non-Hermitian and nonlinear Rice-Mele model. In particular, we uncover how non-Hermiticity 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 framework of the equation of auxiliary eigenvalues, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and non-Hermiticity, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in the real world.

12 pages, 5 figures

References in corpus (95)

• Berry Phase Effects on Electronic Properties
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Formation and Propagation of Matter Wave Soliton Trains
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Topological States and Adiabatic Pumping in Quasicrystals
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Lasing in topological edge states of a 1D lattice
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Probing topological invariants in the bulk of a non-Hermitian optical system
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Nonlinear topological photonics
• Topological nature of nonlinear optical effects in solids
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Simultaneous Observation of Topological Edge State and Exceptional Point in an Open and Non-Hermitian System
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Symmetry and Higher-Order Exceptional Points
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Thouless pumping and topology
• Quantized Nonlinear Thouless Pumping
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Symmetry-protected multifold exceptional points and their topological characterization
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
• Non-Hermitian Linear Response Theory
• Mirror skin effect and its electric circuit simulation
• Exceptional rings protected by emergent symmetry for mechanical systems
• Optical isolation with nonlinear topological photonics
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Quantized Fractional Thouless Pumping of Solitons
• Observation of topological transport quantization by dissipation in fast Thouless pumps
• Nonlinear Thouless pumping: solitons and transport breakdown
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Non-hermitian quantum thermodynamics
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Experimental Observation of a Generalized Thouless Pump with a Single Spin
• Observation of $\mathcal{P}\mathcal{T}$-symmetric quantum coherence in a single ion system
• Interacting quantum fluid in a polariton topological insulator
• Observation of Exceptional Points in Thermal Atomic Ensembles
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Exceptional band touching for strongly correlated systems in equilibrium
• Two-dimensional nonlinear Thouless pumping of matter waves
• Topological origin of quantized transport in non-Hermitian Floquet chains
• Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal Photonic Feedforward Lattices
• Interactions enable Thouless pumping in a nonsliding lattice
• Spontaneous topological pumping in non-Hermitian systems
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Chiral state transfer under dephasing
• Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
• Breakdown of quantization in nonlinear Thouless pumping
• Thouless pumping and trapping of two-component gap solitons
• Topological atomic spinwave lattices by dissipative couplings
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Biorthogonal topological charge pumping in non-Hermitian systems
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Splitting and connecting singlets in atomic quantum circuits
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Frequency Domain Berry Curvature Effect on Time Refraction
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems