The global phase diagram of the 1D SYK model with finite N

We study the generalized SYK model on a 1D lattice with $N$ fermions on each SYK sites and random quadratic coupling between SYK sites.
In the non-interacting case, we find that the random-hopping model with finite $N$ exhibits the Anderson localization, irrespective of the parity of fermion flavor $N$, despite the presence of the chiral symmetry in the model. This is in contrast with the
previous studies where there is evidence of a delocalized (extended) zero-energy mode when $N$ is odd. For the case of finite SYK interactions,
we have performed the exact
diagonalization and show that there is
a dynamic phase transition from many-body localized (MBL) phase to the thermal diffusive metal phase by increasing the strength of the SYK interactions. Moreover, the critical interaction strength for MBL transition decreases with the increase of
fermion flavor $N$.