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- limit. The extended model involves coupling the interacting -site SYK model to a new set of 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 that depends on the fermion filling . The scrambling dynamics throughout the non-Fermi-liquid (NFL) phase is characterized by a universal Lyapunov exponent in the low-temperature limit; however, the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point . The residual entropy at , nonzero in the NFL, also vanishes continuously at the critical point. For the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low-temperature and low-frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent .
5 More- Received 7 November 2016
DOI:https://doi.org/10.1103/PhysRevB.95.134302
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