Quantum chaos and phase transition in the Yukawa-SYK model

Abstract

We analyze the quantum chaotic behavior of the Yukawa-SYK model as a function of filling and temperature, which describes random Yukawa interactions between $N$ complex fermions and $M$ bosons in zero spatial dimensions, for both the non-Fermi liquid and insulating states at finite temperature and chemical potential. We solve the ladder equations for the out-of-time-order correlator (OTOC) for both the bosons and fermions. Despite the appearance of the chemical potential in the Hamiltonian, which explicitly introduces an additional energy scale, the OTOCs for the fermions and bosons in the non-Fermi liquid state turn out to be unaffected, and the Lyapunov exponents that diagnose chaos remain maximal. As the chemical potential increases, the system is known to experience a first-order transition from a critical phase to a gapped insulating phase. We postulate that the boundary of the region in parameter space where each phase is (meta)stable coincides with the curve on which the Lyapunov exponent is maximal. By calculating the exponent in the insulating phase and comparing to numerical results on the boundaries of stability, we show that this is plausible.

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• Lyapunov Exponents, Phase Transitions, and Chaos Bound of ModMax AdS Black Holes
• Non-Fermi liquid fixed point of the dissipative Yukawa-Sachdev-Ye-Kitaev model
• Universal quench dynamics of lattice $q$ fermion Yukawa Sachdev-Ye-Kitaev model
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal