Locality and Heating in Periodically Driven, Power-law Interacting Systems

Abstract

We study the heating time in periodically driven $D$-dimensional systems with interactions that decay with the distance $r$ as a power-law $1/r^{\alpha }$. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for $\alpha >D$. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for $\alpha >2D$. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to $k$-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.

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Cited by in corpus (21)

• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Long-range interacting quantum systems
• Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator
• A Brief History of Time Crystals
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Long-Range Prethermal Phases of Nonequilibrium Matter
• Higher-order and fractional discrete time crystals in clean long-range interacting systems
• Hierarchy of linear light cones with long-range interactions
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Random multipolar driving: tunably slow heating through spectral engineering
• Speed limits and locality in many-body quantum dynamics
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• Lieb Robinson bounds and out of time order correlators in a long range spin chain
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term
• Disordered Lieb-Robinson bounds in one dimension
• Fate of Algebraic Many-Body Localization under driving
• Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems