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

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.