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 $g$.

arXiv comment10 pages; updated funding acknowledgements; version accepted in PRB

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• Classical many-body chaos with and without quasiparticles
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• Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence
• Low temperature quantum bounds on simple models
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model
• Information scrambling and butterfly velocity in quantum spin glass chains
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Wormholes and out-of-time ordered correlators in gauge/gravity duality
• Out-of-time ordered correlation functions for the localized $f$ electrons in the Falicov-Kimball model