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arXiv:2107.07781

Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model

Ancel Larzul, Marco Schirò

Published Jul 16, 2021• 4 citations
arXivHTMLPDF

Abstract

We study the nonequilibrium quench dynamics of a mixed Sachdev-Ye-Kitaev model, with competing two bodies random interactions leading to maximally chaotic Non-Fermi Liquid dynamics and a single body term which dominates at low temperatures and leads to Fermi liquid behavior. For different quench protocols, including sudden switching of two-body interaction and double quench protocols, we solve the large $N$ real-time Dyson equation on the Keldysh contour and compute the dynamics of Green's functions from which we obtain effective temperature and relaxation rates. We show that the model thermalizes to a finite temperature equilibrium and that depending on the value of the quench parameters the effective temperature can be below or above the Fermi-Liquid to Non-Fermi Liquid crossover scale, which can then be accessed through the nonequilibrium dynamics. We identify quench protocols for which the heating dynamics slow down significantly, an effect that we interpret as a signature of prethermalization.

DOI
10.1103/physrevb.105.045105

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We study the nonequilibrium quench dynamics of a mixed Sachdev-Ye-Kitaev model, with competing two bodies random interactions leading to maximally chaotic Non-Fermi Liquid dynamics and a single body term which dominates at low temperatures and leads to Fermi liquid behavior. For different quench protocols, including sudden switching of two-body interaction and double quench protocols, we solve the large NNN real-time Dyson equation on the Keldysh contour and compute the dynamics of Green's functions from which we obtain effective temperature and relaxation rates. We show that the model thermalizes to a finite temperature equilibrium and that depending on the value of the quench parameters the effective temperature can be below or above the Fermi-Liquid to Non-Fermi Liquid crossover scale, which can then be accessed through the nonequilibrium dynamics. We identify quench protocols for which the heating dynamics slow down significantly, an effect that we interpret as a signature of prethermalization.
We study the nonequilibrium quench dynamics of a mixed Sachdev-Ye-Kitaev model, with competing two-body random interactions leading to maximally chaotic non-Fermi liquid dynamics and a single body term which dominates at low temperatures and leads to Fermi liquid behavior. For different quench protocols, including sudden switching of two-body interaction and double quench protocols, we solve the large NNN real-time Dyson equation on the Keldysh contour and compute the dynamics of Green's functions from which we obtain effective temperature and relaxation rates. We show that the model thermalizes to a finite temperature equilibrium and that depending on the value of the quench parameters, the effective temperature can be below or above the Fermi-liquid to non-Fermi liquid crossover scale, which can then be accessed through the nonequilibrium dynamics. We identify quench protocols for which the heating dynamics slow down significantly---an effect that we interpret as a signature of prethermalization.
We study the quantum quench of the Yukawa-Sachdev-Ye-Kitaev model and one of its random hopping extensions with q fermions and one boson. Several equilibrium properties are computed for general q with different parameter scaling within the large- N dynamical mean-field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the random hopping term with constant Yukawa coupling or quenching to different final Yukawa couplings. The postquench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak hopping coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.
We study thermalization dynamics in a fermion-phonon variant of the Sachdev-Ye-Kitaev model coupled to an external cold thermal bath of harmonic oscillators. We find that quantum critical fermions thermalize more efficiently than phonons, in sharp contrast to the behavior in the Fermi liquid regime. In addition, after a short prethermal stage, the system acquires a quasithermal distribution given by a time-dependent effective temperature, reminiscent of ``hydrodynamic'' relaxation. All physical observables relax at the same rate which scales with the final temperature through an exponent that depends universally on the low-energy spectrum of the system and the bath. Such relaxation rate is derived using a hydrodynamic approximation in full agreement with the numerical solution of a set quantum kinetic equations derived from the Keldysh formalism for nonequilibrium Green's functions. Our results hint toward further research on the applicability of the hydrodynamic picture in the description of the late time dynamics of open quantum systems despite the absence of conserved quantities in regimes dominated by conserving collisions.
We study the thermalization, after sudden and slow quenches, in an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to noninteracting lead fermions and can be realized in a graphene flake connected to external leads. A sudden quench to the NFL leads to rapid thermalization via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL shows multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time τ, we find that the excitation energy generated has a remarkable intermediate-τ nonanalytic power-law dependence, τ−η with η<1, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. Our study gives an explicit demonstration of the intriguing contrasts between the out-of-equilibrium dynamics of a NFL and a FL in terms of their thermalization and approach to adiabaticity.
We describe the nonequilibrium quench dynamics of the Sachdev-Ye-Kitaev models of fermions with random all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that, at long times, the fermion two-point function has a thermal form at a final temperature determined by energy conservation, and the numerical analysis is consistent with a thermalization rate proportional to this temperature. We also obtain an exact analytic solution of the quench dynamics in the large qqq limit of a model with qqq fermion interactions: in this limit, the thermalization of the two-point function is instantaneous.
Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.