Scrambling versus relaxation in Fermi and non-Fermi liquids

• URL: http://arxiv.org/abs/2006.02485v2
• Date: Mon, 10 Aug 2020 21:24:26 GMT
• Title: Scrambling versus relaxation in Fermi and non-Fermi liquids
• Authors: Jaewon Kim, Xiangyu Cao, Ehud Altman
• Abstract summary: We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models. 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.
• Score: 1.649000644598787
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $g$.

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