  We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We
show that the chaotic non-Fermi liquid phase described by the ordinary $q = 4$
SYK model has marginally relevant/irrelevant (depending on the sign of the
coupling constants) four-fermion perturbations allowed by symmetry. Changing
the sign of one of these four-fermion perturbations leads to a continuous
chaotic-nonchaotic quantum phase transition of the system accompanied by a
spontaneous time-reversal symmetry breaking. Starting with the SYK$_q$ model
with a $q-$fermion interaction, similar perturbations can lead to a series of
new interacting conformal field theory fixed points.
