  Motivated by the near-horizon geometry of four-dimensional extremal black
holes, we study a disordered quantum mechanical system invariant under a global
$SU(2)$ symmetry. As in the Sachdev-Ye-Kitaev model, this system exhibits an
approximate $SL(2,\mathbb{R})$ symmetry at low energies, but also allows for a
continuous family of $SU(2)$ breaking marginal deformations. Beyond a certain
critical value for the marginal coupling, the model exhibits a quantum phase
transition from the gapless phase to a gapped one and we calculate the critical
exponents of this transition. We also show that charged, rotating extremal
black holes exhibit a transition when the angular velocity of the horizon is
tuned to a certain critical value. Where possible we draw parallels between the
disordered quantum mechanics and charged, rotating black holes.
