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arxiv: 2606.20850 · v1 · pith:FQFJMWXOnew · submitted 2026-06-18 · ❄️ cond-mat.stat-mech · cond-mat.str-el· hep-th· quant-ph

Hydrodynamic tails in chaotic spin chains with quantum group symmetry

Luca V. Delacretaz , Victor Gorbenko , Jiaozi Wang , Bernardo Zan , Aleksandr Zhabin This is my paper

Pith reviewed 2026-06-26 15:11 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.str-elhep-thquant-ph
keywords quantum group symmetryhydrodynamic tailssuperdiffusionspin chainsXXZ modelchaotic dynamicsanomalous transportthermalization
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The pith

Quantum group symmetry protects long-lived transverse spin modes and drives superdiffusion in non-integrable spin chains.

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

The paper establishes that quantum group symmetry can sustain hydrodynamic modes in chaotic many-body systems even when those modes lack any local conserved density. In the XXZ model with added integrability-breaking terms that preserve the symmetry, transverse spin operators exhibit slow power-law decay at high temperature instead of rapid relaxation. The same protection appears in Floquet and classical versions of the dynamics, producing superdiffusive spreading of correlations. This mechanism links generalized symmetries to anomalous transport without requiring integrability. A sympathetic reader would care because it offers a new route to robust hydrodynamic tails in generic thermalizing systems.

Core claim

In non-integrable lattice models that retain quantum group symmetry, such as the XXZ chain with integrability-breaking deformations, local operators carrying U(1) charge display long-lived hydrodynamic tails. Protection by the quantum group symmetry keeps these modes alive despite the absence of local quantum group charge density or current, and the resulting dynamics is superdiffusive in Hamiltonian, Floquet, and classical realizations, with unusual finite-size effects at late times.

What carries the argument

Quantum group symmetry, which shields transverse spin modes from fast decay in the absence of a local conserved density or current.

If this is right

  • Transverse spin dynamics remains superdiffusive rather than diffusive across Hamiltonian, Floquet, and classical realizations.
  • Unusual finite-size effects persist in the relaxation at very late times.
  • The protection applies to other U(1)-charged operators that overlap with the quantum group structure.
  • Similar long-lived modes can appear in any non-integrable model whose deformations leave the quantum group symmetry intact.

Where Pith is reading between the lines

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

  • The same symmetry-protection route could stabilize other non-standard hydrodynamic modes if additional generalized symmetries are realized in chaotic systems.
  • Cold-atom or superconducting-qubit experiments could directly measure the predicted superdiffusive exponent by tracking transverse spin correlations in deformed XXZ chains.
  • This approach suggests a broader classification of anomalous transport based on the type of symmetry that survives integrability breaking.

Load-bearing premise

Integrability-breaking deformations preserve the quantum group symmetry while rendering the model non-integrable.

What would settle it

Observation of purely exponential decay in the late-time transverse spin correlation function of a deformed XXZ chain at high temperature, instead of the predicted power-law superdiffusive tail.

Figures

Figures reproduced from arXiv: 2606.20850 by Aleksandr Zhabin, Bernardo Zan, Jiaozi Wang, Luca V. Delacretaz, Victor Gorbenko.

Figure 1
Figure 1. Figure 1: Spin autocorrelation function Cab(t) = ⟨σ a i (t)σ b i ⟩ in chaotic XXZ-like models with and without quantum group (QG) symmetry, for system sizes L = 22, 26, 30. Both models feature diffusive decay of the longitudinal spin σz, the con￾served density for a conventional U(1) symmetry (inset). In contrast, the decay of transverse spin is markedly different in both models: it is faster than polynomial in the … view at source ↗
Figure 3
Figure 3. Figure 3: Spectral form factor K(t) for the Hamiltonian HQG stag with L = 18, q = 2.57, λ = 1 in the sector {ℓ = 1, m = 1} of size N = 11934. The raw data (light blue) is Gaussian averaged (dark blue) to remove noise and compare to the RMT prediction from Eq. (12) (green). form: KGOE(t) = 1 N    2t tH − t tH log  1 + 2t tH  t ≤ tH 2 − t tH log 2t tH + 1 2t tH − 1 ! t > tH (12) In this expression the Heise… view at source ↗
Figure 4
Figure 4. Figure 4: Infinite temperature autocorrelation function [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Infinite temperature autocorrelation function for [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Infinite-temperature autocorrelation functions [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scaling of the long-time limit C(∞) with system size L for various values of q. Results are shown for (a) the quantum Floquet model at λ = 1.0 and (b) the classical model. Dashed lines indicate fits of the form ∼ L γ . Solid lines indicate the Mazur bound. charge overlaps with the local transverse spin, leading to the bound (at infinite temperature, ρ = 1/2 L) C(∞) ≥ ⟨σ − i E⟩⟨E†σ + i ⟩ ⟨E†E⟩ = 1 L  q + q… view at source ↗
Figure 10
Figure 10. Figure 10: Infinite temperature autocorrelation function [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Infinite temperature autocorrelation function [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Infinite temperature 3pt correlation function [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Infinite-temperature autocorrelation functions [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Infinite-temperature autocorrelation functions [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Infinite temperature autocorrelation function [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: Improved Mazur bound and exact results for [PITH_FULL_IMAGE:figures/full_fig_p013_18.png] view at source ↗
read the original abstract

The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics -- such as superdiffusion -- in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying $U(1)$ charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.

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

0 major / 3 minor

Summary. The manuscript claims that quantum group symmetry protects local U(1)-charged operators (e.g., transverse spin) from rapid decay in non-integrable models, producing long-lived superdiffusive hydrodynamic tails even in the absence of local quantum-group charge densities or currents. This is reported for integrability-breaking deformations of the XXZ chain (Hamiltonian), analogous Floquet circuits, and classical realizations, with additional observations of unusual finite-size effects at late times; the integrable XXZ case is revisited for comparison.

Significance. If the central claim holds, the work supplies a concrete mechanism by which a generalized (quantum-group) symmetry can enforce anomalous hydrodynamics inside genuinely chaotic, non-integrable dynamics. The multi-platform consistency (Hamiltonian, Floquet, classical) and the explicit statement that protection occurs without a local density/current constitute a non-trivial extension beyond conventional hydrodynamic protections. Reproducible numerical evidence across realizations would be a clear strength.

minor comments (3)
  1. [Abstract, §1] Abstract and §1: the statement that the chosen deformations 'preserve the quantum group symmetry while rendering the model non-integrable' is load-bearing; an explicit verification (e.g., commutation of the deformed Hamiltonian with the quantum-group generators) should be shown in a dedicated subsection or appendix.
  2. [Numerical results sections] Numerical sections: error estimates, fitting windows, and data-selection criteria for the reported superdiffusive exponents and late-time tails are not mentioned in the abstract and should be stated clearly (including system sizes and disorder averaging).
  3. [Figures and captions] Figure captions and text: the distinction between 'protection by quantum group symmetry' and conventional hydrodynamic modes should be illustrated with a side-by-side comparison of correlation functions or spectral functions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading and positive evaluation of our work. The recommendation for minor revision is appreciated, and we are pleased that the central claim regarding quantum-group-protected superdiffusive tails in chaotic systems is viewed as a non-trivial extension. Since no specific major comments were raised, we have no point-by-point revisions to address at this stage but remain ready to incorporate any minor suggestions during the revision process.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper asserts that chosen integrability-breaking deformations preserve quantum group symmetry while destroying integrability, and that this symmetry protects long-lived modes without local densities or currents, leading to superdiffusion. No equations, fitted parameters, or self-referential definitions appear in the provided abstract or claim descriptions. The preservation step is stated as a model property rather than derived internally via fit or self-citation chain. The derivation chain is therefore self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient technical detail to enumerate free parameters, axioms, or invented entities; all fields left empty.

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