  We investigate many-body localization in isotropic Heisenberg spin chains
with the local exchange parameters being subject to quenched disorder. Such
systems incorporate a nonabelian symmetry in their Hamiltonian by an invariance
under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the
emergence of a many-body localized phase even in presence of strong disorder.
We report on numerical studies using exact diagonalization for chains of common
spin length 1/2 and 1. The averaged consecutive-gap ratios display a transition
compatible with a crossover from an ergodic phase at small disorder strength to
an incompletely localized phase at stronger disorder. The sample-to-sample
variance of the averaged consecutive-gap ratio displays a maximum at the
transition and distinguishes the incompletely localized phase from a fully
many-body localized phase by its scaling behavior.
