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

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.

4.5 pages, 4 figures + supplemental material

References in corpus (16)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Photovoltaic Hall effect in graphene
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Periodically driven ergodic and many-body localized quantum systems
• Modulated Floquet Topological Insulators
• Anyonic interferometry without anyons: How a flux qubit can read out a topological qubit
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Radial two-dimensional ion crystals in a linear Paul trap
• Proposed Aharonov-Casher interference measurement of non-Abelian vortices in chiral p-wave superconductors
• The Floquet Engineer's Handbook
• Study of the phase diagram of the Kitaev-Hubbard chain
• Dynamical generation of Floquet Majorana flat bands in s-wave superconductors
• Low-frequency and Moiré Floquet engineering: a review