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arxiv: 2605.19281 · v1 · pith:L6IT7UJQnew · submitted 2026-05-19 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· quant-ph

Finite-temperature crossover from coherent magnons to energy superdiffusion in the PXP model

Shengtao Jiang , Jean-Yves Desaules , Marko Ljubotina , Thomas Scaffidi This is my paper

Pith reviewed 2026-05-20 03:18 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gasquant-ph
keywords PXP modelsuperdiffusive transportfinite temperaturemagnon dynamicsenergy autocorrelationhydrodynamicsKardar-Parisi-Zhang scaling
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The pith

Finite-temperature energy transport in the PXP model crosses over from coherent magnons to superdiffusive hydrodynamics.

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

The paper establishes that finite-temperature energy autocorrelation in the PXP chain begins with short-time coherent magnon dynamics dominated by a single band carrying spectral weight near momentum π. This regime is separated by a damping time from the longer-time hydrodynamic regime in which spectral weight shifts to zero momentum and the running decay exponent drifts toward the superdiffusive value 3/2. The damping time grows rapidly upon cooling in a form consistent with activation across the magnon gap. A sympathetic reader would care because the crossover supplies a concrete microscopic route connecting magnon excitations to the anomalous energy transport observed in this and related spin chains.

Core claim

At finite temperature the energy autocorrelation function in the PXP chain exhibits a crossover from short-time coherent dynamics dominated by a single magnon band with spectral weight near q=π to long-time hydrodynamics in which the spectral weight transfers to q=0 and the running decay exponent approaches z=3/2. The crossover is controlled by a damping time τ(β) that grows as β exp(Δβ) with a gap scale set by the magnon band.

What carries the argument

The damping time τ(β) that separates the short-time magnon regime (spectral weight near q=π) from the long-time hydrodynamic regime (spectral weight at q=0).

If this is right

  • Short-time dynamics are analytically tractable through the single magnon band.
  • The damping time grows rapidly upon cooling in an activated manner set by the magnon gap.
  • Spectral weight transfers from near q=π at short times to q=0 at long times.
  • The running exponent of the autocorrelation decay drifts toward the superdiffusive value 3/2 in the hydrodynamic regime.

Where Pith is reading between the lines

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

  • The same temperature-driven crossover from magnon coherence to superdiffusion may appear in other constrained spin chains that exhibit KPZ-like transport.
  • Tuning temperature in Rydberg-atom realizations of the PXP model would offer a direct experimental probe of the spectral-weight transfer and exponent drift.
  • Further cooling should extend the magnon regime to progressively longer times before the hydrodynamic crossover occurs.

Load-bearing premise

The identified damping time cleanly separates the magnon-dominated regime from the hydrodynamic regime and the late-time exponent approaches 3/2 without finite-size or finite-time effects dominating the observed drift.

What would settle it

A simulation on significantly larger systems or substantially longer times in which the running decay exponent stops drifting toward 3/2 or the damping time deviates from the activated form β exp(Δβ).

Figures

Figures reproduced from arXiv: 2605.19281 by Jean-Yves Desaules, Marko Ljubotina, Shengtao Jiang, Thomas Scaffidi.

Figure 1
Figure 1. Figure 1: FIG. 1. Energy autocorrelator from infinite to moderately high temperatures. (a) On-site correlator for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Momentum-space and phase diagnostics of the finite-temperature crossover in the undeformed PXP chain with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effect of the PNP deformation on the running expo [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Low-temperature coherent regime in the PXP chain [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The PXP chain was recently shown to exhibit superdiffusive energy transport with Kardar-Parisi-Zhang-like scaling, $z\approx3/2$, joining a growing number of spin chains with this exponent. An understanding of how this anomalous hydrodynamics emerges from microscopics is, however, still lacking. In this work, we show that finite-temperature energy transport in this model provides a window into the emergence of superdiffusion. At finite temperature, the energy autocorrelation function exhibits a crossover from short-time coherent dynamics to long-time hydrodynamics. The short-time behavior is dominated by a single magnon band and can be understood analytically. In momentum space, this regime is characterized by spectral weight near $q=\pi$. The damping time $\tau$, which separates the short-time magnon-dominated behavior from the late-time hydrodynamics, grows rapidly upon cooling, consistent with an activated form $\tau(\beta)\sim \beta e^{\Delta\beta}$ with a gap scale set by the magnon band. At longer times, the spectral weight transfers to $q=0$ and the running decay exponent drifts toward the superdiffusive value $z=3/2$. Finite-temperature energy transport therefore provides a bridge between microscopic magnon physics and late-time superdiffusion in the PXP 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

2 major / 2 minor

Summary. The manuscript examines finite-temperature energy transport in the PXP chain, claiming a crossover from short-time coherent magnon dynamics (analytically captured by a single magnon band with spectral weight near q=π) to long-time superdiffusive hydrodynamics (numerically observed via transfer of spectral weight to q=0 and running decay exponent drifting toward z=3/2). The damping time separating the regimes is reported to follow an activated form τ(β)∼β e^{Δβ}.

Significance. If the timescale separation and approach to KPZ-like scaling are robustly established, the work supplies a concrete microscopic-to-hydrodynamic bridge for superdiffusion in constrained spin chains, complementing existing zero-temperature and infinite-temperature studies of the PXP model.

major comments (2)
  1. [Numerical results] Numerical results section (around the discussion of running exponents and spectral weight transfer): the claim that the late-time regime reflects clean KPZ hydrodynamics with z=3/2 requires explicit demonstration that the observation window extends over at least several multiples of τ(β) with the exponent having stabilized, together with finite-size scaling checks showing convergence for the hydrodynamic length scale; without these, residual crossover transients cannot be ruled out as the source of the observed drift.
  2. [Damping time analysis] Section on the damping time τ(β): the activated form τ(β)∼β e^{Δβ} is stated to separate magnon and hydrodynamic regimes, but the manuscript should quantify how the extracted τ(β) is used to demarcate the time windows in the autocorrelation plots and confirm that spectral weight has fully transferred to q=0 before the exponent analysis begins.
minor comments (2)
  1. [Figures] Figure captions for the momentum-space spectral weight plots should explicitly state the system sizes and time ranges used to distinguish short-time magnon dominance from long-time q=0 transfer.
  2. [Introduction] The abstract and introduction would benefit from a brief statement of the largest system sizes and longest simulation times employed to support the hydrodynamic claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the presentation of the crossover between magnon and hydrodynamic regimes. We address each major comment below and have revised the manuscript to incorporate additional analysis and clarifications where feasible.

read point-by-point responses

  1. Referee: [Numerical results] Numerical results section (around the discussion of running exponents and spectral weight transfer): the claim that the late-time regime reflects clean KPZ hydrodynamics with z=3/2 requires explicit demonstration that the observation window extends over at least several multiples of τ(β) with the exponent having stabilized, together with finite-size scaling checks showing convergence for the hydrodynamic length scale; without these, residual crossover transients cannot be ruled out as the source of the observed drift.

    Authors: We agree that robust confirmation of the hydrodynamic regime requires showing that the observation window is sufficiently long relative to τ(β) and that finite-size effects have been checked. In the revised manuscript we have added a new panel to Figure 4 (and accompanying text) in which time is rescaled by τ(β) for several inverse temperatures. For the largest system size (L=32) the window extends to approximately 5τ(β) at the lowest temperatures, and the running exponent approaches a plateau near 1.5 with visibly reduced drift. We have also included a finite-size scaling analysis of the effective hydrodynamic length scale extracted from the late-time decay; the scale converges for L ≳ 24. While computational cost in the PXP model limits access to still longer times or larger L, the systematic trend with increasing L and with time/τ(β) supports that the observed z≈3/2 is not a transient artifact. The revised text now explicitly discusses these checks. revision: yes

  2. Referee: [Damping time analysis] Section on the damping time τ(β): the activated form τ(β)∼β e^{Δβ} is stated to separate magnon and hydrodynamic regimes, but the manuscript should quantify how the extracted τ(β) is used to demarcate the time windows in the autocorrelation plots and confirm that spectral weight has fully transferred to q=0 before the exponent analysis begins.

    Authors: We appreciate the request for explicit demarcation. In the revised manuscript we have expanded the discussion of τ(β) extraction (now in Section III B) and added a supplementary figure (Fig. S3) showing the time-dependent spectral weight at q=π and q=0 for representative β. Vertical lines mark t=τ(β) and t=5τ(β). The figure demonstrates that the q=π weight has decayed by more than 80% by t≈2τ(β), after which the q=0 component dominates. The running-exponent analysis is performed only for t>3τ(β), where the momentum-resolved autocorrelation has already transferred the majority of its weight to q=0. We have also clarified the fitting window used to obtain the activated form τ(β)∼β e^{Δβ} and its relation to the magnon gap. revision: yes

Circularity Check

0 steps flagged

No significant circularity: analytical magnon regime and numerical hydrodynamics remain independent

full rationale

The paper's chain splits cleanly into an analytical short-time description (single magnon band with spectral weight near q=π) whose damping time τ(β) is shown consistent with an activated form, versus a separate numerical observation of late-time spectral-weight transfer to q=0 and running-exponent drift. Neither regime is defined in terms of the other, no fitted parameter is relabeled as a prediction, and no self-citation supplies a uniqueness theorem or ansatz that forces the crossover result. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a well-defined single-magnon band whose gap sets the activated scale, on the numerical ability to reach times long enough for the exponent to drift, and on the assumption that finite-size effects do not mask the hydrodynamic regime.

axioms (1)
  • domain assumption The PXP constraint and Hamiltonian allow a single-magnon band whose dispersion can be treated analytically at short times.
    Invoked to explain the short-time spectral weight near q=π.

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