Topological classification of quasiperiodically driven quantum systems

2018/08/23 by Philip J. D. Crowley, Ivar Martin, Anushya Chandran
Mathematics · Physics and Astronomy · #Aperiodic graph #Chern class #Combinatorics #Condensed matter physics #Floquet theory #Lattice (music) #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quasiperiodic function #Spectrum (functional analysis) #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · doi:10.1103/physrevb.99.064306

published as Phys. Rev. B 99, 064306 (2019) · 22 Pages, 15 Figures

arxiv created 2018/08/23 · openalex publication_date 2019/02/28 · arxiv updated 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Few-level quantum systems driven by n_f incommensurate fundamental frequencies exhibit temporal analogs of noninteracting phenomena in n_f spatial dimensions, a consequence of the generalization of Floquet theory in frequency space. We organize the fundamental solutions of the frequency lattice model for n_f=2 into a quasienergy band structure and show that every band is classified by an integer Chern number. In the trivial class, all bands have zero Chern number and the quasiperiodic dynamics is qualitatively similar to Floquet dynamics. The topological class with nonzero Chern bands has dramatic dynamical signatures, including the pumping of energy from one drive to the other, chaotic sensitivity to initial conditions, and aperiodic time dynamics of expectation values. The topological class is however unstable to generic perturbations due to exact level crossings in the quasienergy spectrum. Nevertheless, using the case study of a spin in a quasiperiodically varying magnetic field, we show that topological class can be realized at low frequencies as a prethermal phase, and at finite frequencies using counterdiabatic tools.

Citations

• Diophantine Geometry
• Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
• Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems
• Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field
• Anderson transition in a three-dimensional kicked rotor
• Berry’s phase for energy bands in solids
• Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time
• Photovoltaic Hall effect in graphene
• Quantum Spin Hall Effect in Graphene
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Shortcuts to adiabaticity by counter-diabatic driving
• Materials Design from Nonequilibrium Steady States: Driven Graphene as a Tunable Semiconductor with Topological Properties
• Long-Lived Qubit Memory Using Atomic Ions
• Atomi orientati in campo magnetico variabile
• ON FORMAL QUASI-PERIODIC SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR A TWO-LEVEL SYSTEM WITH A HAMILTONIAN DEPENDING QUASI–PERIODICALLY ON TIME
• Quasi-Periodically Driven Quantum Systems
• Periodic table for Floquet topological insulators
• Steady states of interacting Floquet insulators