Abstract
We describe the non-equilibrium dynamics of the Sachdev-Ye-Kitaev models of fermions with all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that the final state is thermal, and their numerical analysis appears consistent with a thermalization rate proportional to the absolute temperature of the final state. We also obtain an exact analytic solution of the non-equilibrium dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the fermion Green's function is instantaneous.
Highlights
The non-equilibrium dynamics of strongly interacting quantum many-particle systems have been the focus of much theoretical work [1]
A quasiparticle structure has been imposed on the spectral functions, so that the Kadanoff-Baym equations reduce to a quantum Boltzmann equation for the quasiparticle distribution functions
In the following we study the non-equilibrium dynamics described by the time-dependent Hamiltonian in Eq (1.4)
Summary
The non-equilibrium dynamics of strongly interacting quantum many-particle systems have been the focus of much theoretical work [1]. We can obtain non-equilibrium solutions for the Sachdev-Ye-Kitaev (SYK) models [4,5,6] with all-to-all and random interactions between q Majorana fermions on N sites These models are solvable realizations of quantum matter without quasiparticles in equilibrium, and here we shall extend their study to nonequilibrium dynamics. We show from the Kadanoff-Baym equations, and verify by our numerical analysis, that the t → ∞ state is a thermal non-Fermi liquid state at q = 4, which is at an inverse temperature βf = 1/Tf. The value of βf is such that the total energy of the system remains the same after the quench at t = 0+. At low final temperatures, the thermalization rate of the non-Fermi liquid state appears proportional to temperature, as is expected for systems without quasiparticle excitations [12]
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