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arxiv: 2602.02102 · v2 · pith:XPHA3QB7new · submitted 2026-02-02 · ❄️ cond-mat.quant-gas · cond-mat.mes-hall· nlin.PS

Nonreciprocity Induced Fractional Nonlinear Thouless Pumping

Yanqi Zheng , Kun Pu , Ligging Ren , Chenxi Bai , Zhaoxin Liang This is my paper

Pith reviewed 2026-05-22 11:54 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.mes-hallnlin.PS
keywords nonlinear Thouless pumpingnon-Hermitian systemsfractional topologyRice-Mele modelauxiliary eigenvaluesbulk-boundary correspondencenonreciprocitytopological transport
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The pith

Non-Hermiticity induces fractional topological phases in nonlinear Thouless pumping even when linear invariants are quantized.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines Thouless pumping in a non-Hermitian nonlinear Rice-Mele model and shows that nonreciprocity parameters produce fractional topological phases. These phases appear despite the quantized invariants that standard linear calculations would predict. The authors trace the fractional behavior to an auxiliary eigenvalue equation that ties the nonlinear spectrum directly to bulk-boundary correspondence. If this link holds, it supplies a practical route to control edge-state transport by tuning non-Hermitian parameters in driven lattices.

Core claim

In the non-Hermitian nonlinear Rice-Mele model, nonreciprocity induces fractional nonlinear Thouless pumping. This fractional behavior is explained by the auxiliary eigenvalue equation that connects the nonlinear spectral properties to the bulk-boundary correspondence, even when conventional linear approaches yield only quantized invariants.

What carries the argument

The auxiliary eigenvalue equation HΨ=ω S(ω)Ψ, which replaces the standard Schrödinger equation and links nonlinear spectra to topological transport in the non-Hermitian setting.

If this is right

  • Fractional pumping phases become accessible by tuning non-Hermiticity parameters while the underlying lattice remains topologically nontrivial by linear measures.
  • The auxiliary eigenvalue framework supplies a direct way to predict bulk-boundary correspondence in driven nonlinear non-Hermitian systems.
  • Edge-state manipulation in quantum simulators can be achieved through controlled introduction of nonreciprocity.
  • Topological insulators with tunable fractional transport may be engineered by combining nonlinearity and non-Hermiticity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar fractional phases could appear in other driven nonlinear lattices once non-Hermiticity is added, suggesting a broader class of nonreciprocal nonlinear pumps.
  • Experimental platforms with ultracold atoms or photonic waveguides could test the predicted fractional charge by measuring displacement after one pumping cycle.
  • The result hints that linear topological invariants may need systematic nonlinear corrections whenever non-Hermiticity is present.

Load-bearing premise

The auxiliary eigenvalue equation remains valid for the non-Hermitian nonlinear Rice-Mele model and fully determines its topological properties without extra corrections from higher-order terms or boundary effects.

What would settle it

Numerical or experimental measurement of the pumped particle number per cycle taking clearly non-integer values in a non-Hermitian nonlinear lattice under slow periodic driving, or a mismatch between observed edge-state dynamics and predictions from the auxiliary eigenvalue equation.

Figures

Figures reproduced from arXiv: 2602.02102 by Chenxi Bai, Kun Pu, Ligging Ren, Yanqi Zheng, Zhaoxin Liang.

Figure 1
Figure 1. Figure 1: (a) Schematic of the nonlinear non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) The phase diagram of the soliton centroid [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a1)-(d1): The real energy spectrum structure corresponding to the nonlinear non-Hermitian RM Hamiltonian; [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Non-Hermitian control of topological transport: [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates nonlinear Thouless pumping in a non-Hermitian nonlinear Rice-Mele model. It reports that non-Hermiticity parameters induce fractional topological phases even when conventional linear approaches predict quantized invariants, with these fractional phases explained by the auxiliary eigenvalue equation HΨ=ω S(ω)Ψ that links nonlinear spectral features to bulk-boundary correspondence.

Significance. If the central results hold after addressing boundary effects, the work would demonstrate an emergent interplay between nonlinearity and nonreciprocity that produces fractional phases beyond linear topological predictions. This could provide a useful extension of the auxiliary-eigenvalue framework to non-Hermitian settings and inform designs for topological insulators with controllable edge states.

major comments (2)
  1. [Abstract / auxiliary eigenvalue framework] Abstract and the auxiliary-eigenvalue framework section: the claim that the equation HΨ=ω S(ω)Ψ 'naturally explains' the fractional phases and directly supplies bulk-boundary correspondence assumes the auxiliary equation remains unmodified by non-Hermitian skin-effect localization. In open-boundary non-Hermitian nonlinear models the skin effect generically shifts the spectrum; without explicit re-derivation or comparison of periodic-boundary auxiliary spectra against open-boundary numerics, the topological interpretation rests on an unverified assumption.
  2. [Model definition and numerical results] Model and results sections: the manuscript asserts fractional phases appear 'even in the presence of quantized topological invariants as predicted by conventional linear approaches,' yet provides no quantitative comparison (e.g., winding numbers or Chern numbers computed from both linear and auxiliary spectra) that would demonstrate the fractional values are not simply a reparameterization of the same invariant.
minor comments (2)
  1. [Abstract] Abstract: the phrasing 'eigenvalue's nonlinearity-based topological transport' is grammatically awkward and should be revised for clarity.
  2. [References] References: the auxiliary-eigenvalue citations are concentrated among a small set of overlapping authors; adding independent prior works on non-Hermitian nonlinear topology would strengthen the literature context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised regarding the auxiliary eigenvalue framework under non-Hermitian skin effects and the need for quantitative invariant comparisons are valuable. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation and verification of our results.

read point-by-point responses

  1. Referee: [Abstract / auxiliary eigenvalue framework] Abstract and the auxiliary-eigenvalue framework section: the claim that the equation HΨ=ω S(ω)Ψ 'naturally explains' the fractional phases and directly supplies bulk-boundary correspondence assumes the auxiliary equation remains unmodified by non-Hermitian skin-effect localization. In open-boundary non-Hermitian nonlinear models the skin effect generically shifts the spectrum; without explicit re-derivation or comparison of periodic-boundary auxiliary spectra against open-boundary numerics, the topological interpretation rests on an unverified assumption.

    Authors: We agree that the non-Hermitian skin effect in open-boundary conditions could in principle modify the auxiliary eigenvalue equation and that explicit verification is needed to support the bulk-boundary correspondence claim. The auxiliary equation is obtained directly from the nonlinear equations of motion in our model, and the reported fractional phases are observed in open-boundary numerical simulations. To address the concern rigorously, we will add an explicit comparison of the auxiliary spectra under periodic boundary conditions with the open-boundary numerical results, together with a brief re-derivation that accounts for possible skin-effect shifts in the non-Hermitian nonlinear setting. revision: yes

  2. Referee: [Model definition and numerical results] Model and results sections: the manuscript asserts fractional phases appear 'even in the presence of quantized topological invariants as predicted by conventional linear approaches,' yet provides no quantitative comparison (e.g., winding numbers or Chern numbers computed from both linear and auxiliary spectra) that would demonstrate the fractional values are not simply a reparameterization of the same invariant.

    Authors: We acknowledge that a direct quantitative comparison of topological invariants would clarify that the observed fractional phases are distinct from linear predictions rather than a reparameterization. While the fractional character emerges from the nonlinear non-Hermitian dynamics and is not present in the conventional linear invariants, we will add explicit calculations of winding numbers (or equivalent Chern numbers) extracted from both the linear spectrum and the auxiliary eigenvalue equation. This will demonstrate that the fractional values arise specifically from the interplay between nonlinearity and nonreciprocity. revision: yes

Circularity Check

1 steps flagged

Fractional phases rest on auxiliary eigenvalue framework from overlapping-author citations

specific steps
  1. self citation load bearing [Abstract]
    "Crucially, these fractional phases are naturally explained within the framework of the equation of auxiliary eigenvalues $HΨ=ω S(ω)Ψ$ [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 $HΨ=EΨ$ in conservative settings, yet non-Hermitian generalizations remain uncharted."

    The explanation for the novel fractional phases induced by non-Hermiticity parameters is attributed to the auxiliary eigenvalue framework from citations that include the present paper's co-authors (C. Bai and Z. Liang). The bulk-boundary correspondence for the non-Hermitian nonlinear Rice-Mele model is thereby taken as supplied by this prior construction without shown independent validation or modification for nonreciprocity effects in the current work.

full rationale

The paper's central claim—that non-Hermiticity induces fractional topological phases naturally explained by the auxiliary eigenvalue equation linking nonlinear spectra to bulk-boundary correspondence—directly invokes the framework HΨ=ω S(ω)Ψ from prior works that include overlapping authors (C. Bai, Z. Liang). The abstract presents this as the explanatory mechanism without an independent re-derivation or explicit check for non-Hermitian boundary corrections in the current model. This makes the topological interpretation load-bearing on the self-cited construction rather than a fresh derivation from the Rice-Mele Hamiltonian alone. No other circular patterns (e.g., fitted predictions or ansatz smuggling beyond the citation) are evident from the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; full manuscript required to audit the model Hamiltonian and auxiliary equation.

pith-pipeline@v0.9.0 · 5762 in / 1107 out tokens · 40857 ms · 2026-05-22T11:54:36.111298+00:00 · methodology

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