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arxiv: 2604.19041 · v1 · submitted 2026-04-21 · ❄️ cond-mat.str-el · cond-mat.dis-nn

Stealthy hyperuniform disorder: A new route to controlling electric states and magnetic phase transition in correlated systems

Akihisa Koga , Takanori Sugimoto This is my paper

Pith reviewed 2026-05-10 02:12 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.dis-nn
keywords stealthy hyperuniform disorderHubbard modelhoneycomb latticeantiferromagnetic transitiondensity of statesbond disordercorrelated electrons
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The pith

Stealthy hyperuniform bond disorder in the Hubbard model produces a linear density of states and tunes the critical interaction for antiferromagnetic order.

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

The paper examines the Hubbard model on a honeycomb lattice where bond strengths follow a stealthy hyperuniform distribution. This distribution suppresses long-wavelength density fluctuations and leads to a robust linear density of states at low energies. The stealth property modifies wave functions at higher energies and alters the density of states near the band edges. Applying a real-space Hartree approximation reveals that the system transitions from a semimetallic state to an antiferromagnetically ordered state, with the critical interaction strength depending on the degree of stealthiness. This approach differs from random or quasiperiodic disorders in how structural correlations affect the magnetic transition.

Core claim

Stealthy hyperuniform disorder in the bond distribution of the interacting Hubbard model on the honeycomb lattice yields a linear density of states that is robust against the specific stealth properties, while the stealthiness significantly influences the wave functions in higher-energy regions and the density of states near the band edge; consequently, the critical interaction strength for the semimetal-to-antiferromagnet phase transition becomes sensitive to the stealth property, providing a way to control magnetism through structural correlations distinct from quasiperiodic tilings.

What carries the argument

Stealthy hyperuniform bond distribution, a point set with suppressed density fluctuations at small wavevectors, applied to nearest-neighbor bonds to control electronic wavefunctions and interaction-driven magnetism.

If this is right

  • The phase transition always occurs between semimetallic and antiferromagnetically ordered states regardless of the stealth parameter.
  • The critical interaction strength for the transition varies with the stealth property of the bond distribution.
  • The linear density of states persists robustly, but the DOS near the band edge is modified by the stealthiness.
  • Structural correlations in hyperuniform disorder produce different effects on magnetism compared to quasiperiodic honeycomb tilings.

Where Pith is reading between the lines

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

  • Materials engineered with hyperuniform bond disorder could allow tuning of magnetic ordering temperatures without altering the average lattice geometry.
  • Further studies with more advanced methods beyond Hartree approximation might reveal whether the tunability persists in the presence of quantum fluctuations.
  • Similar disorder types could be explored in other lattice models to control different phases like superconductivity or charge ordering.

Load-bearing premise

The real-space Hartree approximation accurately captures the magnetic phase transition and its dependence on the stealth property in this disordered interacting system.

What would settle it

Exact diagonalization or quantum Monte Carlo simulations on finite systems with stealthy hyperuniform bond distributions would show if the critical interaction strength matches the Hartree prediction or deviates significantly.

Figures

Figures reproduced from arXiv: 2604.19041 by Akihisa Koga, Takanori Sugimoto.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Honeycomb lattice and its unit vectors [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Upper panels show the distributions of the bonds for the honeycomb systems with (a) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Four kinds of vertices in the honeycomb lattice with [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Density of states for the tightbinding model with [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Bond distribution for the K-pattern with [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Average of local magnetizations as a function of the [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Distribution of the local magnetizations in Hubbard model [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: shows the IPR of the magnetizations in the systems with randomly disordered and stealthy hyperuniform bonds. When U/t ∼ 6, the corresponding curves are almost identical for both IPR1 and IPR2, which is consistent with the fact that the local magnetizations have comparable magnitudes and similar distributions (see [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Distribution of stealthy hyperuniform bonds with [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. (a) DOS for the tightbinding model with [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
read the original abstract

We investigate the effects of stealthy hyperuniform bond distributions on the electronic and magnetic properties of the Hubbard model on the honeycomb lattice. Hyperuniform structures, distinct from random and quasiperiodic ones, have recently attracted considerable interest due to their anomalous suppression of density fluctuations. By diagonalizing the noninteracting Hamiltonian, we show that a linear density of states (DOS) robustly emerges, while the stealth property of the bond distribution changes the wave functions in the higher-energy region extended and significantly modifies the DOS near the band edge. To clarify the impact on magnetism, we apply the real-space Hartree approximation to the Hubbard model. We find that, the phase transition always occurs between semimetallic and antiferromagnetically ordered states and its critical interaction strength is sensitive to the stealth property. A comparison with the quasiperiodic honeycomb tiling further highlights the role of structural correlations. These results demonstrate that stealthy hyperuniform disorder provides a novel route to controlling electronic states and magnetic phase transitions in correlated systems.

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

1 major / 1 minor

Summary. The manuscript investigates stealthy hyperuniform bond disorder in the Hubbard model on the honeycomb lattice. Non-interacting properties are obtained by direct diagonalization, yielding a robust linear DOS with stealth-induced modifications to higher-energy wave functions and band-edge DOS. Interacting properties are studied via the real-space Hartree approximation, which finds a semimetal-AF transition for all distributions examined but with critical interaction strength sensitive to the stealth property; a comparison to quasiperiodic tiling is included to highlight structural correlations.

Significance. If the reported sensitivity of the magnetic transition to stealth survives beyond mean-field, the work would establish hyperuniform disorder as a distinct control parameter for correlated phases, separate from random or quasiperiodic cases. The non-interacting diagonalization results constitute a clear strength, delivering direct, parameter-free information on DOS and wave-function properties. The overall significance is reduced by the lack of validation for the interacting approximation in a 2D system where fluctuations are expected to matter.

major comments (1)
  1. The claim that the critical interaction strength for the semimetal-AF transition is sensitive to the stealth property rests entirely on the real-space Hartree approximation (described in the abstract and the section on the interacting Hubbard model). This static mean-field treatment neglects dynamical fluctuations and nonlocal correlations, which are known to renormalize the transition in the 2D honeycomb Hubbard model. No error bars, convergence tests, or benchmarks against exact diagonalization or quantum Monte Carlo are reported, so the quantitative sensitivity to stealth remains an uncontrolled approximation.
minor comments (1)
  1. The title uses 'electric states' while the abstract correctly employs 'electronic states'; this inconsistency should be corrected.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive criticism. We address the major comment on the interacting approximation below and have revised the manuscript accordingly to clarify the scope and limitations of our results.

read point-by-point responses

  1. Referee: The claim that the critical interaction strength for the semimetal-AF transition is sensitive to the stealth property rests entirely on the real-space Hartree approximation (described in the abstract and the section on the interacting Hubbard model). This static mean-field treatment neglects dynamical fluctuations and nonlocal correlations, which are known to renormalize the transition in the 2D honeycomb Hubbard model. No error bars, convergence tests, or benchmarks against exact diagonalization or quantum Monte Carlo are reported, so the quantitative sensitivity to stealth remains an uncontrolled approximation.

    Authors: We agree that the real-space Hartree approximation constitutes a static mean-field treatment that omits dynamical fluctuations and nonlocal correlations known to renormalize the semimetal-AF transition in the clean 2D honeycomb Hubbard model. Our calculations demonstrate that, within this approximation, the critical interaction strength remains sensitive to the stealth property of the bond disorder, while the transition itself stays between semimetallic and antiferromagnetically ordered states. We do not assert that the quantitative sensitivity survives beyond mean-field; the results are presented as findings obtained with this method, which permits treatment of large disordered systems. Benchmarks against quantum Monte Carlo or exact diagonalization for the interacting disordered case are not included, as such comparisons are computationally intensive for the relevant system sizes and ensemble averages. In the revised manuscript we will (i) qualify the abstract and the relevant sections to state explicitly that critical values are obtained within the Hartree approximation, (ii) add a dedicated paragraph discussing the expected influence of fluctuations by reference to the clean-limit literature, and (iii) report convergence tests with system size together with iteration tolerances and associated error estimates. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives its claims via direct numerical diagonalization of the noninteracting Hamiltonian (yielding linear DOS and stealth-dependent wavefunction/DOS modifications) followed by self-consistent real-space Hartree solution of the interacting model (yielding semimetal-AF transition with stealth-sensitive critical U). Neither step reduces by construction to a fitted input, self-definition, or load-bearing self-citation; the quantitative sensitivity emerges from the numerics rather than being imposed. Comparison to quasiperiodic tilings is external. This is a standard computational workflow with independent content, warranting score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; no explicit free parameters, new entities, or ad-hoc axioms are stated. The Hartree treatment is treated as a standard domain tool.

axioms (1)
  • domain assumption The real-space Hartree approximation sufficiently describes the antiferromagnetic transition in the presence of stealthy hyperuniform disorder.
    Invoked to obtain the magnetic phase diagram from the interacting Hamiltonian.

pith-pipeline@v0.9.0 · 5480 in / 1137 out tokens · 40010 ms · 2026-05-10T02:12:27.122676+00:00 · methodology

discussion (0)

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Reference graph

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