Spin Survival Probability as a Probe of Dynamics in Infinite-Temperature Strongly Bond-Disordered 1D Chains

The on-site survival probability of an initially oriented spin as a function of time in infinite-temperature, or equivalently randomly initialized, disordered systems has become accessible in various experimental settings. Certain universal properties are computable in one-dimensional disordered systems using the formalism of the strong-disorder renormalization group (SDRG). We show that, even at very strong disorder, SDRG is only capable of predicting the long-time asymptotic approach of this function rather than its value at infinite time, the latter being sensitive to the precise structure of the localized eigenfunctions. We corroborate this result with extensive numerical studies for the nearest-neighbor bond-disordered XX spin chain. We also extend our investigation to one-dimensional spin chains with long-range interactions under positional disorder: while no SDRG approach appears available for such models, numerical results for the survival probability at accessible system sizes suggest the same form of long-time asymptotic approach. We comment on possible ways in which the survival probability may probe many-body localization.