Scrambling versus relaxation in Fermi and non-Fermi liquids

Abstract

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 $1/\tau$ and the Lyapunov exponent ${\lambda }_L$ characterizing scrambling. In the Fermi liquid states we find that the quasi-particle relaxation rate dictates the Lyapunov exponent. In non-Fermi liquids, where $1/\tau \gg T$, we find that ${\lambda }_L$ 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. ${\lambda }_L$ approaches the general upper bound $2\pi T$ 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 $\sim g\ln (1/g)$ of the coupling constant $g$.

10 pages; updated funding acknowledgements; version accepted in PRB

References in corpus (1)

• Quantum chaos on a critical Fermi surface

Cited by in corpus (4)

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• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Information scrambling and butterfly velocity in quantum spin glass chains
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