Half-integer quantized topological response in quasiperiodically driven quantum systems

TL;DR

This paper demonstrates that a strongly driven quantum system exhibits a half-integer quantized topological response at a transition point, revealing universal scaling and connecting topological phenomena with non-equilibrium dynamics.

Contribution

It introduces the concept of half-integer quantized topological response in quasiperiodically driven systems and provides universal scaling functions for energy transfer at the transition.

Findings

Half-integer quantization of the pumping rate at the transition.

Universal Kibble-Zurek scaling functions for energy transfer.

Identification of qubit experiments to observe these phenomena.

Abstract

A spin strongly driven by two harmonic incommensurate drives can pump energy from one drive to the other at a quantized average rate, in close analogy with the quantum Hall effect. The pumping rate is a non-zero integer in the topological regime, while the trivial regime does not pump. The dynamical transition between the regimes is sharp in the zero-frequency limit and is characterized by a Dirac point in a synthetic band structure. We show that the pumping rate is {\em half-integer} quantized at the transition and present universal Kibble-Zurek scaling functions for energy transfer processes. Our results adapt ideas from quantum phase transitions, quantum information and topological band theory to non-equilibrium dynamics, and identify qubit experiments to observe the universal linear and non-linear response of a Dirac point in synthetic dimensions.