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.

References in corpus (7)

• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• More on Supersymmetric and 2d Analogs of the SYK Model
• Large $N$ theory of critical Fermi surfaces
• Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors
• Quantum Phase Transition in the Yukawa-SYK Model
• Maximal quantum chaos of the critical Fermi surface
• Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence

Cited by in corpus (7)

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• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• 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