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arxiv: 2508.01564 · v3 · submitted 2025-08-03 · ❄️ cond-mat.mes-hall

Unconventional Altermagnetism in Quasicrystals: A Hyperspatial Projective Construction

Yiming Li , Mingxiang Pan , Jun Leng , Yuxiao Chen , Huaqing Huang This is my paper

Pith reviewed 2026-05-19 01:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords altermagnetismquasicrystalsHubbard modelNéel orderspin splittingAmmann-Beenker latticePenrose latticequasiperiodic systems
0
0 comments X

The pith

Quasicrystals host g-wave and h-wave altermagnetism through interaction-induced Néel order on projected lattices.

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

The paper uses a hyperspatial projection method to build decorated Ammann-Beenker and Penrose quasicrystalline lattices that contain inequivalent sublattices. An anisotropic Hubbard model on these lattices develops Néel order when interactions are turned on, and the resulting electronic states show spin-polarized spectral functions that alternate according to the quasicrystal's octagonal or decagonal rotational symmetry. This produces unconventional altermagnetism with g-wave and h-wave character whose spin splitting respects the noncrystallographic symmetries. A sympathetic reader would care because the result shows that compensated, momentum-dependent spin splitting can occur in aperiodic systems that lack the translational periodicity required by ordinary crystals.

Core claim

Using a hyperspatial projective construction, decorated Ammann-Beenker and Penrose quasicrystalline lattices with inequivalent sublattices are obtained. On these lattices an anisotropic Hubbard model supports interaction-induced Néel order that generates alternating spin-polarized spectral functions reflecting the underlying quasicrystalline symmetry, thereby realizing g-wave (octagonal) and h-wave (decagonal) altermagnetism. Symmetry analysis together with a low-energy effective theory confirms that the altermagnetic spin splitting remains compatible with the quasicrystalline rotational symmetries.

What carries the argument

The hyperspatial projection framework that produces decorated quasicrystalline lattices with inequivalent sublattices, on which an anisotropic Hubbard model with interaction-induced Néel order yields symmetry-protected, momentum-dependent spin splitting.

If this is right

  • Altermagnetism is possible in systems that lack translational periodicity.
  • Spin splitting with g-wave and h-wave character can be stabilized by quasicrystalline rotational symmetries.
  • Quasicrystals supply a setting for magnetisms and transport effects that have no direct counterpart in periodic crystals.
  • The low-energy theory derived from the model describes the unconventional spin splitting that survives in the quasiperiodic regime.

Where Pith is reading between the lines

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

  • Artificial quasicrystals realized in cold-atom or photonic platforms could be used to test whether the predicted alternating spin polarization appears.
  • The same projection technique might be applied to other aperiodic tilings to generate additional unconventional altermagnetic symmetries.
  • Because the spin splitting is tied to rotational symmetry rather than periodicity, it may remain robust against certain types of disorder that would destroy conventional altermagnetism.

Load-bearing premise

The anisotropic Hubbard model parameters continue to capture the connectivity and symmetry of the lattices when the system is taken to the quasiperiodic limit.

What would settle it

A numerical or experimental spectral function on a decorated Penrose lattice that fails to display h-wave alternating spin polarization once Néel order is established would falsify the claim.

Figures

Figures reproduced from arXiv: 2508.01564 by Huaqing Huang, Jun Leng, Mingxiang Pan, Yiming Li, Yuxiao Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the hyperspatial projective construction of the quasicrystal lattice for altermagnetism. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Order parameter [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Penrose tiling lattice with two sublattices (A [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) (b) Initial ABT in (a) the physical and (b) perpendicular space. (c) (d) The 1st order hopping (green lines) and [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) (b) Initial Penrose tiling in (a) the physical space and (b) the perpendicular space. (c) All possible 1st-order [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Decorated ABT quasicrystalline lattice constructed via the cut-and-project method. Purple and yellow points denote [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Mean-field results for the decorated ABT quasicrystal. The parameters are [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Mean-field results for the decorated Penrose tiling. (a) Phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Spectral functions of the ABT quasicrystal with nonzero staggered magnetization but without decorations: [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Spectral function of the Penrose quasicrystal with nonzero staggered magnetization but without decorations: [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Acceptance windows for different hopping vectors [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Spin-polarized eigenvalues around the Γ point described by the AM terms (a) [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Distribution of [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. (a) Eigenvalues of energy for HOTI in a finite octagonal sample with system size [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. (a) Mass term [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
read the original abstract

Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend the concept of altermagnetism to quasicrystals -- aperiodic systems with long-range order and noncrystallographic rotational symmetries. Using a hyperspatial projection framework, we construct decorated Ammann-Beenker and Penrose quasicrystalline lattices with inequivalent sublattices and investigate a Hubbard model with anisotropic hopping. We demonstrate that interaction-induced N\'eel order on such lattices gives rise to alternating spin-polarized spectral functions that reflect the underlying quasicrystalline symmetry, revealing the emergence of unconventional $g$-wave (octagonal) and $h$-wave (decagonal) altermagnetism. Our symmetry analysis and low-energy effective theory further reveal unconventional altermagnetic spin splitting, which is compatible with quasicrystalline rotational symmetry. Our work shows that quasicrystals provide a fertile ground for realizing unconventional altermagnetic phases beyond crystallographic constraints, offering a platform for novel magnetisms and transport phenomena unique to quasiperiodic 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 / 2 minor

Summary. The manuscript extends altermagnetism to quasicrystals via a hyperspatial projective construction of decorated Ammann-Beenker and Penrose lattices with inequivalent sublattices. It applies an anisotropic Hubbard model, demonstrates interaction-induced Néel order producing alternating spin-polarized spectral functions that reflect quasicrystalline symmetry, and identifies unconventional g-wave (octagonal) and h-wave (decagonal) altermagnetism. Symmetry analysis and a low-energy effective theory are used to establish compatibility of the spin splitting with noncrystallographic rotational symmetries.

Significance. If the central results hold, the work provides a concrete route to altermagnetism in aperiodic systems, expanding the concept beyond crystallographic constraints and identifying new platforms for momentum-dependent spin splitting and associated transport effects in quasicrystals. The explicit construction of lattices supporting g- and h-wave character, together with the symmetry analysis, constitutes a clear advance over prior periodic-crystal studies.

major comments (1)
  1. [Hyperspatial projection framework] Hyperspatial projection framework (model construction section): The central claim that interaction-induced Néel order yields spin splitting reflecting quasicrystalline symmetry rests on the anisotropic Hubbard model faithfully capturing nearest-neighbor connectivities and rotational symmetries of the projected lattices without renormalization or emergent long-range terms in the quasiperiodic limit. Explicit checks (e.g., comparison of finite approximants to the infinite limit or derivation of the effective hopping matrix) are needed to confirm that the projection does not introduce symmetry-breaking corrections that would alter the reported g- and h-wave character.
minor comments (2)
  1. [Low-energy effective theory] The abstract refers to 'low-energy effective theory' without specifying the approximations or cutoff; the main text should include a dedicated paragraph or appendix deriving the effective model and stating its range of validity.
  2. [Numerical results] Figure captions for spectral-function plots should explicitly state the interaction strength U/t, temperature, and system size (or approximant order) used, to allow direct comparison with the claimed Néel order.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of our work and for the constructive major comment. We address the point below and agree that additional verification strengthens the central claims.

read point-by-point responses

  1. Referee: [Hyperspatial projection framework] Hyperspatial projection framework (model construction section): The central claim that interaction-induced Néel order yields spin splitting reflecting quasicrystalline symmetry rests on the anisotropic Hubbard model faithfully capturing nearest-neighbor connectivities and rotational symmetries of the projected lattices without renormalization or emergent long-range terms in the quasiperiodic limit. Explicit checks (e.g., comparison of finite approximants to the infinite limit or derivation of the effective hopping matrix) are needed to confirm that the projection does not introduce symmetry-breaking corrections that would alter the reported g- and h-wave character.

    Authors: We agree that explicit verification of the projection's fidelity is important. Our hyperspatial construction maps nearest-neighbor connectivities and local environments directly from the higher-dimensional periodic lattice, with the projection direction and decoration chosen to preserve the quasicrystalline rotational symmetries exactly. The anisotropic hopping is defined on these projected bonds without additional renormalization. To address the concern, we have now performed explicit comparisons of the spin-polarized spectral functions across finite approximants of increasing size for both the Ammann-Beenker and Penrose cases; the g-wave and h-wave spin-splitting patterns converge without introducing symmetry-breaking corrections. We have also derived the effective hopping matrix in the quasiperiodic limit via the cut-and-project formalism, confirming the absence of emergent long-range terms that would alter the reported altermagnetic character. We will incorporate these checks and the derivation into a revised manuscript, for example as an expanded section on the model construction or a dedicated appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper constructs decorated quasicrystalline lattices via a hyperspatial projection method and then studies an anisotropic Hubbard model on those lattices. Interaction-induced Néel order is shown to produce spin-polarized spectral functions with g-wave or h-wave character that reflect the quasicrystalline symmetry. This is presented as a numerical or analytical outcome of the model rather than a quantity defined in terms of itself or fitted parameters that are then relabeled as predictions. No load-bearing self-citation chains, self-definitional steps, or ansatz smuggling are identifiable from the provided text. The central result follows from applying the Hubbard model to the projected lattices and analyzing the resulting spectral functions, which constitutes independent content.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the hyperspatial projection for generating quasicrystalline lattices with two sublattices, the applicability of the anisotropic Hubbard model to these lattices, and the assumption that interaction-driven Néel order survives in the quasiperiodic setting.

free parameters (1)
  • anisotropic hopping amplitudes
    Direction-dependent hopping parameters in the Hubbard model are introduced to match the quasicrystalline geometry; their specific values are not stated in the abstract.
axioms (2)
  • domain assumption Hyperspatial projection preserves the required rotational symmetries and produces inequivalent sublattices suitable for altermagnetic order.
    Invoked when the authors state they construct the lattices and investigate the Hubbard model on them.
  • domain assumption The Hubbard interaction is sufficient to stabilize Néel order whose spin texture respects the quasicrystalline point-group symmetry.
    Central to the claim that interaction-induced order produces the reported g-wave and h-wave splitting.

pith-pipeline@v0.9.0 · 5750 in / 1627 out tokens · 29379 ms · 2026-05-19T01:51:24.542346+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Anomalous thermoelectric and thermal Hall effects in irradiated altermagnets

    cond-mat.mes-hall 2026-02 unverdicted novelty 7.0

    Elliptically polarized light irradiation converts d-wave altermagnets into Chern insulators, yielding quantized thermal Hall conductivity and gap-edge peaks in the thermoelectric Hall response.

  2. Layer Hall effect induced by altermagnetism

    cond-mat.mes-hall 2026-01 unverdicted novelty 7.0

    D-wave altermagnets on Bi2Se3 surfaces induce a layer Hall effect with zero net Hall conductance for antiparallel Néel vectors and a quantized Chern state for parallel vectors.

Reference graph

Works this paper leans on

121 extracted references · 121 canonical work pages · cited by 2 Pith papers · 1 internal anchor

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    Lattice construction and Hopping Geometry for Quasicrystals In this section, we will show that both the vertices and edges on the Ammann-Beenker and Penrose tilings, which correspond to the orbital sites and hoppings in the 2D quasicrystal lattice, can be generated from the hypercubic lattice by the cut-and-project method. a. Ammann-Beenker tiling Ammann-...

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    Decoration induced anisotropic intra-sublattice hoppings a. Decoration from hyperspace To realize the altermagnetism in the quasicrystal lattice with two sublattices, we added several decoration sites to make the A and B sublattices globally inequivalent. Taking the ABT quasicrystal as an example, we translate all B vertices by (1/2,1/2,1/2,1/2) in hyperc...

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    The altermagnetic Hubbard model We consider two species of fermionic atoms labeled by spin s in an ABT quasicrystalline lattice described by the following altermagnetic Hubbard model ˆH=− X ⟨i,j⟩,s (tijˆc† isˆcjs +h.c.) +U X i ˆni↑ˆni↓ =− X ⟨iA,jB⟩,s t1(ˆc† iAsˆcjBs + ˆc† jBs ˆciAs)− X ⟨iα,jα⟩,s tαα(r)ˆc† iαsˆcjαs +U X iα ˆniα↑ˆniα↓, (B1) where ˆc(†) is =...

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    Order parameter and ansatz We apply a self-consistent Hartree-Fock (HF) method to characterize the magnetic order of the system. For this purpose, we introduce the N´ eel order parameter, δm= 1 2N X i∈A ⟨ˆni↑ −ˆni↓⟩ − X i∈B ⟨ˆni↑ −ˆni↓⟩ ! ,(B2) where capital lettersA(B) in the summation denote the set of sublattices A (B) andNdenotes the number of sites. ...

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    =U (X i∈A [(n+δm)ˆni↓ + ˆni↑(n−δm)] + X i∈B [(n−δm)ˆni↓ + ˆni↑(n+δm)] ) + const

    The mean-field treatment With the ansatz (B3) of the occupation number and the mean-field approximation ˆn i↑ˆni↓ ≈ ⟨ˆni↑⟩ˆni↓ + ˆni↑⟨ˆni↓⟩ − ⟨ˆni↑⟩⟨ˆni↓⟩, the interacting term can be reduced to a decoupled form in terms of the order parameter: U X i ˆni↑ˆni↓ ≈U X i [⟨ˆni↑⟩ˆni↓ + ˆni↑⟨ˆni↓⟩] + const. =U (X i∈A [(n+δm)ˆni↓ + ˆni↑(n−δm)] + X i∈B [(n−δm)ˆni↓...

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    The self-consistent process can be expressed in the following steps:

    Self-consistent process We solve the real-space mean-field equations by self-consistently determining the order parameterδmas well as the chemical potentialµ, which is set by solving the equationn= 1 2N P i⟨ˆni↑ + ˆni↓⟩under a fixed particle number. The self-consistent process can be expressed in the following steps:

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    Make an initial guess onδmand obtain the initial mean-field HamiltonianH s =H 0 + (−1)sHHF int whereH HF int is defined by Eq. (B6)

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    ,2Nlabels 2N eigenstates for the mean-field Hamiltonian

    Diagonalize the mean-field Hamiltonian to obtain 2Nwavefunctions,ψ a, wherea= 1,2, . . . ,2Nlabels 2N eigenstates for the mean-field Hamiltonian. Each wavefunctionψ a is a 2N-dimensional vector, which reads ψa = (ca1↑, ca2↑, . . . , ca1↓, ca2↓, . . .)T, wherec ais are c-numbers

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    Update chemical potentialµand order parameterδm. Explicit expressions of them can be derived as follows: with given wavefunctions, the occupation numbers can be expressed by: ⟨ˆnis⟩=⟨ˆc† isˆcis⟩= 2NX a=1 f(ϵ a −µ)⟨ψ a|ˆc† isˆcis|ψa⟩= 2NX α=1 c∗ aiscaisf(ϵ a −µ) (B7) wheref(ϵ−µ) = e−β(ϵ−µ)+1 −1 withβ= 1/k BTis the Fermi-Dirac distribution. With Eq. (B7), t...

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    Calculate the deviation between the newδmand the old one, if the derivation is small enough, end the iteration and outputδm, otherwise, go back to step-1 and use the updatedδmas the new input. 12

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    We evaluate the order parameterδmas a function ofU/t 1 and ¯t2/t1 forδ 2 = 0.2 in an ABT quasicrystal withN= 329 sites

    Numerical results Our calculations are performed at half-filling,n= 1 2N P i⟨ˆni↑ + ˆni↓⟩= 1/2, although the resulting phase diagram remains stable under slight doping. We evaluate the order parameterδmas a function ofU/t 1 and ¯t2/t1 forδ 2 = 0.2 in an ABT quasicrystal withN= 329 sites. The results are presented in Fig. 7, witht 1 = 1, ¯t2 = (t2r +t 2b)/...

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    Therefore, it does not support altermagnetism based on the previous analysis of magnetic point groups in crystals

    Decorated Ammann-Beenker tiling By directly considering the spin arrangement on the ABT quasicrystal, theC 8z rotational symmetry only correlates vertices within sublattice A or B, meaning the corresponding operation is{C 8z; 1}, and no operation includes time reversal. Therefore, it does not support altermagnetism based on the previous analysis of magnet...

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    Decorated Penrose tiling Let{e 1, e2 ,e3, e4, e5}be the basis vectors of a 5D hypercubic lattice. The coordinates of the A and B sublattices are denoted as : X=(n 1, n2, n3, n4, n5)≡ 5X i=1 niei, X∈ ( Aif P i ni ∈2Z, Bif P i ni ∈2Z+ 1, (D3) The decorations are achieved by translating all vertices of sublattice B by a vector ofv= 1 2(1, 1, 1, 1, 1), and th...

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    The 16 itinerant electrons have a Kondo couplingJto the collinear local moments, which have staggered magnetization N=M A −M B

    Mean-field Hamiltonian Now, we express the mean-field Hamiltonian as HMF = X iα (−1)η−1N·σc † iαciα − X ⟨iα,jβ⟩ (tβα(rji)c† jβ ciα +h.c.) =N·σ( X RA c† RA cRA − X RB c† RB cRB)− X ⟨RA,RB ⟩ t1 c† RA cRB +c † RB cRA − X (R′α−Rα)∈Rr NN t2rc† Rα cR′α − X (R′α−Rα)∈Rb NN t2bc† Rα cR′α , (E1) whereiαdenote thei-th site with positionR i belonging to sublatticeα=A...

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    quasicrystal

    Low-energy effective theory Having obtained the mean-field Hamiltonian, we explore the momentum-dependent spin splitting in its electronic structure, which is a key characteristic of altermagnetism. However, since the QL possesses long-range orientational order but lacks translational symmetry, we cannot use the Bloch theorem as for the crystal calculatio...

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    Discussion about Orthogonality in Quasicrystals In this section, we take the ABT as an example to discuss the orthogonality in quasicrystals, as mentioned in Eq. (E5). Consider a 4D hyperlattice with widthLand bond lengtha. SinceL/a≫1 in the thermodynamic limit, the Fourier transform takes a simple form: Z dξ X {mi} δ(ξ− X i miei)e−iΠ·ξ = 1 a4 X H∈L δ(Π−H...

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