Thermalization of many many-body interacting Sachdev-Ye-Kitaev models
Jan C. Louw, Stefan Kehrein
Abstract
We investigate the nonequilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the $q\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where $q/2$ denotes the order of the random Dirac fermion interaction. We extend previous results by Eberlein et al. [Phys. Rev. B 96, 205123 (2017)] to show that a single SYK $q\ensuremath{\rightarrow}\ensuremath{\infty}$ Hamiltonian for $t\ensuremath{\ge}0$ is a perfect thermalizer in the sense that the local Green's function is instantaneously thermal. The only memories of the quantum state for $t<0$ are its charge density and its energy density at $t=0$. Our result is valid for all quantum states amenable to a $1/q$ expansion, which are generated from an equilibrium SYK state in the asymptotic past and acted upon by an arbitrary combination of time-dependent SYK Hamiltonians for $t<0$. Importantly, this implies that a single SYK $q\ensuremath{\rightarrow}\ensuremath{\infty}$ Hamiltonian is a perfect thermalizer even for nonequilibrium states generated in this manner.