Low-energy level spacing and entropy change across SYK non-Fermi liquid to a Fermi Liquid transition for finite-N

We study a quantum phase transition (QPT) between a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) and a Fermi liquid in a solvable large-N model where the zero-temperature residual entropy of the NFL vanishes continuously at the QPT in the large-N limit. We show via exact diagonalization that, even at finite-N, the QPT manifests itself in the system-size scaling of low-energy level spacings above the ground state. The evidence of this QPT is also directly visible in the single-particle Greens function and, indirectly, in the thermalization dynamics after a quench. Interestingly, we find that the QPT has little effect on the entanglement entropy in the ground state. We also construct the effective low-energy field theory across the QPT by considering fluctuations around the large-N limit.