2020/06/30 by Jaewon Kim, Xiangyu Cao, Ehud Altman · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevb.102.085134
published as Phys. Rev. B 102, 085134 (2020) · 10 pages; updated funding acknowledgements; version accepted in PRB
arxiv created 2020/08/10 · arxiv updated 2020/08/26
We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large N, allows us to clarify the relations between the quasi-particle relaxation rate 1/τ and the Lyapunov exponent λL characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where 1/τ≫ T, we find that λL is always T-linear with a prefactor that is independent of the coupling constant in the limit of weak coupling. Instead it is determined by a scaling exponent that characterizes the relaxation rate. λL approaches the general upper bound 2πT at the transition to a fast scrambling state. Finally in a marginal Fermi liquid state the exponent is linear in temperature with a prefactor that vanishes as a non analytic function ∼ g ln (1/g) of the coupling constant g.