Fibonacci steady states in a driven integrable quantum system

TL;DR

This paper investigates the non-equilibrium steady states of an integrable quantum system under Fibonacci driving, revealing quasiperiodic residual energy oscillations and bounded state trajectories on the Bloch sphere.

Contribution

It introduces a Fibonacci driving protocol for an integrable quantum system and analyzes its high-frequency steady state behavior and fluctuations.

Findings

System reaches a non-equilibrium steady state at high frequency

Residual energy oscillates quasiperiodically between two values

State trajectories are bounded between two concentric circles on the Bloch sphere

Abstract

We study an integrable system that is reducible to free fermions by a Jordan-Wigner transformation which is subjected to a Fibonacci driving protocol based on two non-commuting Hamiltonians. In the high frequency limit $\omega \to \infty$, we show that the system reaches a non-equilibrium steady state, up to some small fluctuations which can be quantified. For each momentum $k$, the trajectory of the stroboscopically observed state lies between two concentric circles on the Bloch sphere; the circles represent the boundaries of the small fluctuations. The residual energy is found to oscillate in a quasiperiodic way between two values which correspond to the two Hamiltonians that define the Fibonacci protocol. These results can be understood in terms of an effective Hamiltonian which simulates the dynamics of the system in the high frequency limit.