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arxiv: 2606.05837 · v1 · pith:SWB72ZRTnew · submitted 2026-06-04 · ❄️ cond-mat.str-el · cond-mat.mes-hall· cond-mat.mtrl-sci

Odd-parity magnons in the Haldane-Hubbard model from topological exciton condensation

Rintaro Eto , Johannes Knolle This is my paper

Pith reviewed 2026-06-27 23:42 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallcond-mat.mtrl-sci
keywords Haldane-Hubbard modeltopological excitonsodd-parity magnonsNéel stateodd-wave magnetsexciton condensationf-wave splittingmagnon topology
0
0 comments X

The pith

Condensation of topological excitons drives the paramagnetic phase into a collinear Néel state that realizes an odd-wave magnet with odd-parity magnons showing f-wave splitting.

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

The paper establishes that topological excitons exist in the paramagnetic phase of the Haldane-Hubbard model and condense to produce the transition into collinear Néel order. This order forms an odd-wave magnet whose magnons carry odd parity and split according to an f-wave pattern. Electron bandgap closing forces a corresponding magnon gap closing that alters magnon topology and enlarges the spin splitting. A sympathetic reader would care because the mechanism ties exciton condensation directly to magnetic order and to new forms of magnon behavior that the model predicts can appear in driven systems.

Core claim

The condensation of topological excitons in the paramagnetic phase drives the transition into the collinear Néel state that realizes an odd-wave magnet with odd-parity magnons displaying a characteristic f-wave splitting. An electron bandgap closing ensures magnon bandgap closing causing a change in odd-parity magnon topology, as well as a drastically enlarged spin splitting.

What carries the argument

Topological exciton condensation that links the paramagnetic phase to the collinear Néel state and fixes the odd-parity magnon spectrum.

Load-bearing premise

Exciton condensation is the main driver of the transition to Néel order and the magnon spectrum follows directly from this process without other interaction channels or finite-size effects changing the reported parity and splitting.

What would settle it

A calculation of the magnon dispersion relations inside the Néel phase that shows neither f-wave splitting nor the predicted change in odd-parity magnon topology when the electron gap closes would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.05837 by Johannes Knolle, Rintaro Eto.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the odd-parity-wave magnetism in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Exciton Berry curvature of the lowest bands with [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a),(d),(g) Electron bands near the nontopological-topological AFM phase boundary obtained with Hartree-Fock approximation. Red, [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Odd-wave magnets are the counterparts to even-wave altermagnets realizing odd-parity spin splitting. Normally discussed for noncollinear systems, they have recently been shown to appear in collinear magnetic states in the presence of loop currents. Here we study collective excitations of the paramagnetic and magnetic phase of the seminal Haldane-Hubbard model. We identify the existence topological excitons in the paramagnetic phase, and their condensation as the driving mechanism into the collinear N\'{e}el state. The latter realizes an odd-wave magnet with odd-parity magnons displaying a characteristic $f$-wave splitting. We further uncover that an electron bandgap closing ensures magnon bandgap closing causing a change in odd-parity magnon topology, as well as a drastically enlarged spin splitting. Our results establish the presence of topological excitons and odd-parity magnons in the Haldane-Hubbard, with potential realizations in Floquet-driven materials and cold atomic gases.

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 paper claims that in the Haldane-Hubbard model, topological excitons exist in the paramagnetic phase and their condensation drives the transition to a collinear Néel state. This state realizes an odd-wave magnet featuring odd-parity magnons with a characteristic f-wave splitting. Additionally, an electron bandgap closing is shown to cause a magnon bandgap closing, leading to a change in the topology of odd-parity magnons and a drastically enlarged spin splitting. The results suggest potential realizations in Floquet-driven materials and cold atomic gases.

Significance. If the results hold, the work provides a mechanism linking topological exciton condensation to the emergence of odd-parity magnons in collinear systems, extending the concept of odd-wave magnets. It offers insights into the interplay between electronic topology and magnetic excitations in a paradigmatic model, with relevance to experimental platforms like Floquet engineering and ultracold atoms.

major comments (2)
  1. [Paramagnetic phase analysis] The claim that exciton condensation drives the Néel transition requires demonstration that it is the dominant instability; the manuscript should include comparisons of susceptibilities or critical points for competing orders to substantiate this.
  2. [Magnon spectrum extraction] The reported f-wave splitting and topology change in magnons tied to electron gap closing may be affected by omitted interaction channels or finite-size effects; the paper should specify the method (e.g., RPA, Bethe-Salpeter) and provide convergence checks or error estimates.
minor comments (2)
  1. Ensure consistent use of terminology such as 'odd-wave magnet' and 'odd-parity magnons' throughout the text.
  2. [Abstract] The abstract mentions 'loop currents' in the introduction to odd-wave magnets; a brief reference to prior work on this would help contextualize.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive assessment of the significance of our work. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Paramagnetic phase analysis] The claim that exciton condensation drives the Néel transition requires demonstration that it is the dominant instability; the manuscript should include comparisons of susceptibilities or critical points for competing orders to substantiate this.

    Authors: We agree that explicitly comparing the exciton instability to competing channels would strengthen the claim that condensation drives the transition. The manuscript identifies topological excitons in the paramagnetic phase and links their condensation to the Néel state, but does not present a full comparison of susceptibilities. In the revised manuscript we will add RPA calculations of the critical points (or susceptibilities) for the leading competing orders, such as charge-density-wave instabilities, within the same framework to demonstrate dominance. revision: yes

  2. Referee: [Magnon spectrum extraction] The reported f-wave splitting and topology change in magnons tied to electron gap closing may be affected by omitted interaction channels or finite-size effects; the paper should specify the method (e.g., RPA, Bethe-Salpeter) and provide convergence checks or error estimates.

    Authors: The magnon spectrum is obtained from the poles of the transverse spin susceptibility evaluated in the random-phase approximation (RPA) in the Néel phase (see Sec. III and the methods). We will make this explicit in the revision. While the presented results are robust across the parameter range studied, we acknowledge that additional finite-size scaling and estimates of neglected channels would be valuable; the revised version will include these checks and error estimates. revision: partial

Circularity Check

0 steps flagged

No circularity: claims rest on model calculations without definitional reduction or fitted predictions

full rationale

The abstract and provided context describe identifying topological excitons in the paramagnetic phase of the Haldane-Hubbard model and their condensation as the mechanism into the collinear Néel state, followed by analysis of odd-parity magnons. No equations are presented that would allow checking for self-definitional loops (e.g., order parameter defined via the condensation it is claimed to drive) or for a fitted parameter being relabeled as a prediction. No self-citations are invoked as load-bearing uniqueness theorems. The derivation chain therefore remains self-contained against external benchmarks such as the standard Haldane-Hubbard Hamiltonian and standard many-body techniques, with no reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities that can be extracted. All ledger entries are therefore empty.

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Forward citations

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