SYK Model, Chaos and Conserved Charge

Abstract

We study the SYK model with complex fermions, in the presence of an all-to-all $q$-body interaction, with a non-vanishing chemical potential. We find that, in the large $q$ limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential $\mu$. Even when the coupling $J$, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of $\mu$ which are exponentially small compared to $J$ lead to suppression of the Lyapunov exponent.

18pages, 4 figures, v2:references and acknowledgment added, typos corrected

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• Spectral form factor in the double-scaled SYK model
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Holography, quantum complexity and quantum chaos in different models