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arXiv:2605.19281 · Physical review. B./Physical review. B

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

Shengtao Jiang, Jean-Yves Desaules, Marko Ljubotina, Thomas Scaffidi

cond-mat.stat-mechcond-mat.quant-gasquant-phSubmitted May 19, 2026• Announced May 20, 2026• 0 citations
v1 · May 19, 2026v2 · May 26, 2026v3 · Aug 21, 2026
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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 $q=π$. The damping time $τ$, which separates the short-time magnon-dominated behavior from the late-time hydrodynamics, grows rapidly upon cooling, consistent with an activated form $τ(β)\sim βe^{Δβ}$ 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.

Journal reference
Phys. Rev. B 114, 084306 (2026)
DOI
10.1103/mx9k-1mc6
Comments
8 pages, 4 figures; comments are welcome

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The PXP chain was recently shown to exhibit superdiffusive energy transport with Kardar-Parisi-Zhang-like scaling, z≈3/2z\approx3/2z≈3/2, 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=πq=πq=π. The damping time τττ, which separates the short-time magnon-dominated behavior from the late-time hydrodynamics, grows rapidly upon cooling, consistent with an activated form τ(β)∼βeΔβτ(β)\sim βe^{Δβ}τ(β)∼βeΔβ with a gap scale set by the magnon band. At longer times, the spectral weight transfers to q=0q=0q=0 and the running decay exponent drifts toward the superdiffusive value z=3/2z=3/2z=3/2. Finite-temperature energy transport therefore provides a bridge between microscopic magnon physics and late-time superdiffusion in the PXP model.
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Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.
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Using the framework of generalized hydrodynamics for integrable systems, the authors study finite-temperature transport in the 1D Hubbard model. At strong coupling, the authors characterize transport in the spin-incoherent regime -- where spin degrees of freedom are ``hot'' while charge degrees of freedom are ``cold'' -- and its crossover to the Luttinger liquid regime. Furthermore, using a combination of analytical arguments and numerical simulations, the authors show that when the Hamiltonian features a spin or $\ensuremath{\eta}$-pairing SU(2) symmetry or both, spin or charge transport is superdiffusive with Kardar-Parisi-Zhang scaling.
A bstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time tE∗ {t}_E^{\ast } tE∗​ t E ∗ = c cr K , for the Krylov chain of finite length K , and c cr = O (1). In particular, we find a scaling ~ K 1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K −2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/ N ) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.
We construct a family of chaotic brickwork quantum circuits exhibiting superdiffusive transport with dynamical exponent z=3/2z=3/2z=3/2 in the full Kardar--Parisi--Zhang (KPZ) universality class. This is enabled by the equilibrium current associated with a inhomogeneous conserved density having a nontrivial dependence on the chemical potential. Using nonlinear fluctuating hydrodynamics, we derive the propagation velocity, broadening scale, and universal scaling form of the charge correlation function from microscopic equilibrium properties. Tensor-network simulations of a two-site spin-111 (qutrit) circuit reproduce these parameter-free predictions, including the full stationary KPZ profile. We further construct a three-site spin-12\frac1221​ (qubit) circuit, where transport varies from diffusive to superdiffusive with the chemical potential, while long-lived coherent quasiparticles delay the convergence of the profile to the KPZ scaling form. Our results establish that KPZ superdiffusion in quantum systems is not restricted to fine-tuned integrable models.