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Quench, thermalization, and residual entropy across a non-Fermi liquid to Fermi liquid transition

Arijit Haldar, Prosenjit Haldar, Surajit Bera, Ipsita Mandal, Sumilan Banerjee

Published Jan 1, 2020• 28 citations
OpenAlex

Abstract

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.

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arXiv:2011.05238•Physical review. B./Physical review. B•Sep 20, 2021•22 citations
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.
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.
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the complex-valued SYK model at temperature TTT coupled to a zero temperature reservoir by a quench. We find out that the tunneling current dynamics reveals a way to distinguish the SYK non-Fermi liquid (nFL) initial state of the subsystem from the disordered Fermi liquid. Temperature dependent contribution to the current's half-life scales linearly in TTT at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as T2T^2T2. This provides a characteristic signature of the SYK non-Fermi liquid in a non-equilibrium measurement.
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.
While bound states are typically treated as long-lived quasiparticles with slow momentum and current relaxation in a Fermi liquid (FL) phase, this paper investigates their properties within a non-Fermi liquid (NFL) phase exhibiting Sachdev–Ye–Kitaev (SYK)-like ensemble behavior. We establish a fundamental relation between the UV cutoff of the relative scattering momentum, [Formula: see text], and the emergence of this SYK-like physics, a connection which has not been previously explored. We find that [Formula: see text] directly controls the statistical properties of the coupling term. In the limit [Formula: see text], the large number of momentum steps causes the coupling to behave as a Gaussian or Chi-square random variable, fulfilling the conditions for SYK-like chaos. This reveals [Formula: see text] as a tuning parameter for a phase transition: the [Formula: see text] limit corresponds to the NFL phase with ill-defined bound states, while a finite [Formula: see text] corresponds to a (disordered) FL phase with well-defined bound state quasiparticles. Furthermore, we show that pair condensation, which emerges at a critical temperature, competes with and suppresses the NFL phase. Finally, we note that in the case of large-range condensation, a homogeneous character emerges and thermalization is observed, where high-energy eigenstates show low overlap with low-entanglement states.
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g., quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this paper we consider the complex-valued SYK model at initial temperature TTT and chemical potential $\ensuremath{\mu}$ coupled to a large reservoir by a quench at time t=0t=0t=0. The reservoir is kept at zero temperature and charge neutrality. We find that the dynamics of the discharging process of the SYK quantum dot reveals a distinctive characteristic of the SYK non-Fermi liquid (nFl) state. In particular, we focus on the tunneling current induced by the quench. We show that the temperature dependent contribution to the current's half-life scales linearly in TTT at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as T2{T}^{2}T2.