Many-Body Localization with Quasiperiodic Driving

Abstract

Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\ge 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\ge 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically-driven setting, and verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.

15 pages, 4 figures + 6 pages, 4 figures; (v2) Clarifications on synthetic localization

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Cited by in corpus (22)

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• Dynamical localization and slow dynamics in quasiperiodically-driven quantum systems
• Topological frequency conversion in Weyl semimetals
• Localization persisting under aperiodic driving
• Geometric Floquet theory
• Hilbert-Space Ergodicity in Driven Quantum Systems: Obstructions and Designs
• Anomalous Random Multipolar Driven Insulators
• Localization of matter waves in lattice systems with moving disorder
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Controllable Floquet edge modes in a multi-frequency driving system
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Engineering Hierarchical Symmetries
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• Stable time rondeau crystals in dissipative many-body systems
• Absence of disordered Thouless pumps at finite frequency
• Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Topological energy pumping in a quasi-periodically driven four-level system
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model