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arxiv: 2606.26222 · v1 · pith:C7ZH2M2Pnew · submitted 2026-06-24 · ❄️ cond-mat.str-el

The fate of odd-parity magnetism in one dimension

Kasper Rettedal Eikeland , Sondre Duna Lundemo , Asle Sudb{\o} This is my paper

Pith reviewed 2026-06-26 01:11 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords p-wave magnetodd-parity magnetismbosonizationLuttinger liquidsKondo couplingspectral functionone-dimensional chaincommensurate filling
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0 comments X

The pith

A one-dimensional p-wave magnet produces quasi-long-range order that gives electrons a p-wave spectral function at commensurate fillings.

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

The authors study a chain of electrons in an extended Hubbard model coupled by Kondo interaction to a chain of local moments arranged in an odd-parity magnetic pattern. They use bosonization to describe the coupled system as two Luttinger liquids. The local-moment chain develops algebraic order that matches the symmetry of the p-wave magnet. This order sets a commensurability condition on the electron filling, which activates extra interaction terms in the bosonic theory. Those terms make the electron spectral function display p-wave character, an effect that disappears when the filling is incommensurate.

Core claim

In the bosonized theory the spin chain acquires quasi long-range order consistent with the combined time-reversal and translation symmetry of the p-wave magnet. This order imposes a commensurability condition on the electronic filling under which additional interactions appear. These interactions give the electron spectral function a pronounced p-wave character. Away from commensurate filling the interactions are irrelevant and the p-wave character is lost.

What carries the argument

Coupled Luttinger liquids obtained by bosonizing the Kondo-coupled extended Hubbard model, with the magnetic order enforcing commensurability.

If this is right

  • Quasi long-range order appears in the spin chain matching the p-wave magnet symmetry.
  • Additional interactions arise in the bosonic field theory at commensurate electronic filling.
  • The electron spectral function acquires p-wave character due to these interactions.
  • The p-wave character disappears away from commensurate filling as the interactions become irrelevant.

Where Pith is reading between the lines

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

  • Similar filling-dependent effects might occur in other one-dimensional magnetic systems where order sets commensurability.
  • This suggests that signatures of odd-parity magnetism in spectra are density-selective in one dimension.
  • The result could guide searches for p-wave magnets in engineered atomic chains or nanowires.

Load-bearing premise

The classical configuration of the local moments already contains the key features of an odd-parity magnet, and the bosonization approach works in the weak-coupling limit of the combined system.

What would settle it

If angle-resolved photoemission spectroscopy on a one-dimensional realization of this model at the commensurate filling shows no p-wave asymmetry in the spectral function, the predicted imprinting effect would be ruled out.

Figures

Figures reproduced from arXiv: 2606.26222 by Asle Sudb{\o}, Kasper Rettedal Eikeland, Sondre Duna Lundemo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the system governed by the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scaling dimensions of the operators [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Weak-coupling phase diagram in terms of the onsite interaction [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Electron spectral function at quarter filling for (a-b) positive chirality of the spin chain [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

We consider a one-dimensional model for a $p$-wave magnet within the bosonization framework. The model consists of itinerant electrons described by an extended Hubbard model coupled to a chain of localized moments through the Kondo exchange. The classical ground state of the local-moment system captures the salient features of an odd-parity magnet. By bosonizing the coupled system, a description in terms of coupled Luttinger liquids follows, giving rise to a rich weak-coupling phase diagram. It is shown that the spin chain develops quasi long-range order consistent with the combined time-reversal and translation symmetry defining the $p$-wave magnet. We highlight the peculiar role played by this order in establishing a commensurability condition on the electronic filling under which additional interactions appear in the bosonic field theory. It is demonstrated that these interactions endow the electron spectral function with a pronounced $p$-wave character. Away from commensurate filling, these interactions are rendered irrelevant and the ensuing $p$-wave character is lost.

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 / 1 minor

Summary. The manuscript analyzes a one-dimensional model of itinerant electrons (extended Hubbard) Kondo-coupled to localized moments. The local moments are placed in their classical ground state realizing odd-parity p-wave magnetism under combined time-reversal and translation. Bosonization yields coupled Luttinger liquids whose phase diagram exhibits quasi-long-range order in the spin sector consistent with the p-wave symmetry. At commensurate electron filling this order generates additional relevant interactions that impart p-wave character to the electron spectral function; the character is lost at incommensurate fillings.

Significance. If the central assumptions hold, the work supplies a controlled weak-coupling description of how odd-parity magnetic order can imprint on the single-particle spectrum of a 1D Kondo lattice. The explicit construction of the commensurability condition and the resulting operator content in the bosonic theory constitute a concrete, falsifiable prediction for spectral features.

major comments (2)
  1. [Model and bosonization setup] The analysis begins by fixing the local-moment chain to its classical ground state (abstract and model section). In one dimension this configuration is subject to strong quantum fluctuations that are not parametrically suppressed by the Kondo coupling or any implicit inter-moment exchange. No renormalization-group stability analysis or comparison with the quantum spin-chain spectrum is provided to show that the assumed p-wave order survives. Because the commensurability condition and the p-wave spectral features are derived directly from this background, the validity of the entire weak-coupling phase diagram rests on an unverified approximation.
  2. [Bosonization and phase diagram] The bosonization is performed around the classical local-moment configuration. It is not shown how the Kondo term is treated when the local moments are themselves dynamical quantum spins; in particular, whether the effective Luttinger-liquid parameters remain perturbative or acquire non-perturbative renormalizations from the spin sector is left unaddressed.
minor comments (1)
  1. [Abstract] The abstract states that the spin chain develops QLRO 'consistent with' the p-wave symmetry; the precise symmetry-allowed operators and their scaling dimensions should be listed explicitly in the bosonized Hamiltonian.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive criticism. We address the two major comments below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Model and bosonization setup] The analysis begins by fixing the local-moment chain to its classical ground state (abstract and model section). In one dimension this configuration is subject to strong quantum fluctuations that are not parametrically suppressed by the Kondo coupling or any implicit inter-moment exchange. No renormalization-group stability analysis or comparison with the quantum spin-chain spectrum is provided to show that the assumed p-wave order survives. Because the commensurability condition and the p-wave spectral features are derived directly from this background, the validity of the entire weak-coupling phase diagram rests on an unverified approximation.

    Authors: We agree that the stability of the assumed p-wave order against quantum fluctuations of the local moments is not demonstrated in the manuscript. The classical configuration is adopted as an input to define the symmetry background for the subsequent bosonization analysis of the electron sector. In the revised manuscript we will add an explicit statement in the model section and introduction clarifying that all results are conditional on the persistence of this order, and that a full RG treatment of the coupled quantum spin-electron system lies outside the present scope. revision: yes

  2. Referee: [Bosonization and phase diagram] The bosonization is performed around the classical local-moment configuration. It is not shown how the Kondo term is treated when the local moments are themselves dynamical quantum spins; in particular, whether the effective Luttinger-liquid parameters remain perturbative or acquire non-perturbative renormalizations from the spin sector is left unaddressed.

    Authors: The bosonization is performed with the local moments fixed in the classical p-wave configuration, which sets the background for the Kondo coupling. When the moments are treated as fully dynamical quantum spins, additional non-perturbative effects on the Luttinger parameters could arise. We will revise the text to state this limitation explicitly and to emphasize that the reported phase diagram and spectral features are obtained within the classical-moment approximation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard bosonization to explicitly defined model

full rationale

The paper constructs an explicit Hamiltonian (extended Hubbard + Kondo coupling to local moments), adopts the classical ground state of the moment chain as an input assumption, and performs standard bosonization to obtain coupled Luttinger liquids. No quoted step equates a derived quantity to a fitted parameter or prior self-citation by construction; the commensurability condition and p-wave spectral features emerge from the resulting bosonic operators rather than being presupposed. The classical-ground-state assumption is an uncontrolled approximation whose validity is external to the derivation itself, not a circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of bosonization to the coupled system and the assumption that the classical local-moment ground state encodes the essential symmetry properties of the p-wave magnet; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Bosonization framework applies to the coupled itinerant electrons and local moments in the weak-coupling limit
    The paper states that bosonizing the coupled system yields coupled Luttinger liquids and a weak-coupling phase diagram.
  • domain assumption Classical ground state of the local-moment chain captures the salient features of an odd-parity magnet
    The abstract explicitly invokes this to set up the model before bosonization.

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discussion (0)

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