  The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study
non-Fermi liquid properties, holographic duality and maximally chaotic
behavior. In this work, we consider a generalization of the SYK model that
contains two SYK models with different number of Majorana modes coupled by
quadratic terms. This model is also solvable, and the solution shows a
zero-temperature quantum phase transition between two non-Fermi liquid chaotic
phases. This phase transition is driven by tuning the ratio of two mode
numbers, and a Fermi liquid non-chaotic phase sits at the critical point with
equal mode number. At finite temperature, the Fermi liquid phase expands to a
finite regime. More intriguingly, a different non-Fermi liquid phase emerges at
finite temperature. We characterize the phase diagram in term of the spectral
function, the Lyapunov exponent and the entropy. Our results illustrate a
concrete example of quantum phase transition and critical regime between two
non-Fermi liquid phases.
