Studying many-body localization in exchange-coupled electron spin qubits using spin-spin correlations

We show that many-body localization (MBL) effects can be observed in a finite chain of exchange-coupled spin qubits in the presence of both exchange and magnetic noise, a system that has been experimentally realized in semiconductors and is a potential solid-state quantum computing platform. In addition to established measures of MBL, the level spacing ratio and the entanglement entropy, we propose another quantity, the spin-spin correlation function, that can be measured experimentally and is particularly well-suited to experiments in semiconductor-based electron spin qubit systems. We show that, in cases that the established measures detect as delocalized ``phases,'' the spin-spin correlation functions retain no memory of the system's initial state (i.e., the long-time value deviates significantly from the initial value), but that they do retain memory in cases that the established measures detect as localized ``phases.'' We also discover an interesting counterintuitive result that there is no clear tendency towards localization with increasing charge noise in small systems ($3--10$ spins). The proposed experiments should be feasible in the existing semiconductor spin qubit systems.