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We characterise and study dynamical localisation of a finite interactingquantum many-body system. We present explicit bounds on the disorder strengthrequired for the onset of localisation of the dynamics of arbitrary ensemble ofsites of the XYZ spin-1/2 model. We obtain these results using a novel form ofthe fractional moment criterion, which we establish, together with ageneralisation of the self-avoiding walk representation of the system Green'sfunctions, called path-sums. These techniques are not specific to the XYZ modeland hold in a much more general setting. We further present bounds for twoobservable quantities in the localised regime: the magnetisation of anysublattice of the system as well as the linear magnetic response function ofthe system. We confirm our results through numerical simulations.

An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System