Fluctuation-dissipation relations as an experimentally accessible indicator for thermalization of disordered quantum spin systems

Non-integrable closed quantum systems are generally expected to thermalize in the sense that local observables take thermal ensemble values in the long-time limit. In disordered systems striking exceptions to this behavior, such as many-body localized phases, can occur. A sufficient condition for the approach to thermal equilibrium is eigenstate thermalization, which is, however, hard to check experimentally. Eigenstate thermalization implies that fluctuation-dissipation relations (FDR) should hold, relating the system's thermal fluctuations with how perturbations on the system dissipate. FDRs are experimentally accessible through response measurements and may offer a measurable indicator for thermalization. In this talk, we present numerical results on the validity FDRs in disordered quantum spin systems and discuss experimental protocols for measuring them. The concrete system under consideration is a Rydberg spin system, which presents a versatile platform for realizing Heisenberg models of tunable anisotropy and external fields, different geometries, and tunable disorder strength.