Solvable model for a dynamical quantum phase transition from fast to slow scrambling

Abstract

We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi liquid like state, while still allowing an exact solution in a suitable large $N$ limit. The extended model involves coupling the interacting $N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low energy phase below a critical ratio of peripheral sites $p<p_c(n)$ that depends on the fermion filling $n$. The scrambling dynamics throughout the non-Fermi liquid phase is characterized by a universal Lyapunov exponent $λ_L\to 2πT$ in the low temperature limit, however the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point $p_c$. The residual entropy at $T\to 0$, non zero in the NFL, also vanishes continuously at the critical point. For $p>p_c$ the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low temperature and frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent $λ_L\propto T^2$.

20 pages, 12 figures, added the calculation for Lyapunov exponent away from the particle-hole symmetric situation