Steady states of a quasiperiodically driven integrable system

TL;DR

This paper investigates the long-term behavior of a quasiperiodically driven integrable quantum spin system, revealing a unique nonequilibrium steady state that differs from known ensembles, with implications for understanding complex quantum dynamics.

Contribution

It demonstrates the emergence of a novel steady state in a quasiperiodically driven integrable system, not described by traditional ensembles, and explores its dependence on system parameters.

Findings

A new steady state forms after exponentially long times.

The steady state is neither a generalized Gibbs ensemble nor an infinite temperature state.

Sensitivity of the steady state to driving parameters is shown in a toy model.

Abstract

Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we consider a prototypical integrable spin system, the spin-$1/2$ transverse field Ising model in one dimension, in a pulsed magnetic field. The time dependence of the field is taken to be quasiperiodic by choosing the pulses to be of two types that alternate according to a Fibonacci sequence. We show that a novel steady state emerges after an exponentially long time when local properties (or equivalently, reduced density matrices of subsystems with size much smaller than the full system) are considered. We use the temporal evolution of certain coarse-grained quantities in momentum space to understand this nonequilibrium steady state in more detail and show that unlike the previously known cases, this steady state is neither described by a periodic generalized Gibbs ensemble nor by an infinite temperature ensemble. Finally, we study a toy problem with a single two-level system driven by a Fibonacci sequence; this problem shows how sensitive the nature of the final steady state is to the different parameters.