Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology

TL;DR

This paper introduces Floquet gauge pumps, a method using periodically driven Hamiltonians to detect spectral degeneracies linked to symmetry or topology in quantum systems, demonstrated in a driven XY model.

Contribution

It presents the novel concept of Floquet gauge pumps and shows how they can reveal ground-state degeneracies through dynamically generated currents in a driven spin model.

Findings

Floquet Hamiltonian includes static XY and dynamic Dzyaloshinsky-Moriya interactions.

Magnetization current depends on phases of complex couplings, revealing degeneracies.

Experimental setup with trapped ions can realize the Floquet gauge pump.

Abstract

We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, the current reveals the ground-state degeneracies that distinguish the ordered and disordered phases. We discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions.