Thermal Diffusivity and Pole-Skipping in the Incoherent Semilocally Critical IR

Abstract: Pole-skipping offers compelling evidence for the hydrodynamic origin of chaotic behavior in strongly coupled quantum systems. We demonstrate that the cumulative effect of higher-order corrections to the hydrodynamic diffusive mode, captured by the parameter $\Omega$, determines the thermal diffusivity through chaos parameters, providing new insights into the interplay between chaos and hydrodynamics. In the incoherent limit, where momentum relaxation is pronounced, we show that the thermodynamically stable phase corresponds to a semi-locally critical IR fixed point. This finding extends previous analyses of simple IR fixed points and may offer a gravity dual description for stable phases beyond the Sachdev-Ye-Kitaev model in the incoherent regime. Additionally, we connect our findings to a universal bound on the thermal diffusion constant in holography, establishing a direct link with the dynamical critical exponent $z$. We derive a new relation, $\Omega = (2-z)/(2z-2)$, and propose that it characterizes the thermodynamically stable phase for generic values of $z$.