  We determine the global renormalization group (RG) flow of the
Sachdev-Ye-Kitaev (SYK) model. This flow allows for an understanding of the
surprising role of critical slowing down at a quantum first-order transition in
strongly-correlated electronic systems. From a simple truncation of the
infinite hierarchy of the exact functional RG flow equations we identify
several fixed points: Apart from a stable fixed point, associated with the
celebrated non-Fermi liquid state of the model, we find another stable fixed
point related to an integer-valence state. These stable fixed points are
separated by a discontinuity fixed point with one relevant direction,
describing a quantum first-order transition. Most notably, the fermionic
spectrum continues to be quantum critical even at the discontinuity fixed
point. This rules out a description of this quantum first-order transition in
terms of a local effective Ising variable that is established for classical
transitions. It reveals that quantum phase coexistence can be a genuine
critical state of matter.
