Thermalization of many many-body interacting SYK models

TL;DR

This paper demonstrates that in the large-q limit, a single SYK Hamiltonian can instantaneously thermalize local Green's functions for a wide class of non-equilibrium states, extending previous results.

Contribution

It extends prior work by showing that a single SYK q→∞ Hamiltonian acts as a perfect thermalizer for all states generated from equilibrium via time-dependent Hamiltonians.

Findings

Single SYK q→∞ Hamiltonian thermalizes local Green's functions instantaneously.

Thermalization applies to all states generated from equilibrium via time-dependent Hamiltonians.

Memory of initial state is limited to charge and energy densities at t=0.

Abstract

We investigate the non-equilibrium dynamics of complex Sachdev-Ye-Kitaev (SYK) models in the $q\rightarrow\infty$ 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 $q\rightarrow\infty$ Hamiltonian for $t\geq 0$ 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 $q\rightarrow\infty$ Hamiltonian is a perfect thermalizer even for non-equilibrium states generated in this manner.