Exponentially slow heating in periodically driven many-body systems (1507.01474v2)

Abstract: We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that for systems with local interactions, energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including decay of highly energetic excitations in cold atomic and solid-state systems.

• The paper shows that energy absorption in locally driven many-body systems decays exponentially with increased drive frequency.
• The authors utilize Lieb-Robinson bounds and rigorous proofs to establish quantitative limits for both local and global driving cases.
• The findings suggest that high-frequency drives can stabilize Floquet many-body phases by suppressing heating, offering practical guidelines for experiments.

Overview of "Exponentially Slow Heating in Periodically Driven Many-Body Systems"

The paper "Exponentially Slow Heating in Periodically Driven Many-Body Systems" by Dmitry A. Abanin, Wojciech De Roeck, and François Huveneers investigates the behavior of periodically driven quantum systems, particularly focusing on the energy absorption properties of such systems under periodic driving. The authors derive general bounds on the linear response energy absorption rates for various many-body systems, specifically those comprising spins or fermions on a lattice. This paper contributes to the broader understanding of how periodically driven systems, especially those with local interactions, experience exponentially slow heating as the frequency of driving increases.

Main Contributions

1. Exponential Decay of Energy Absorption: The paper shows that, in systems with local interactions, the energy absorption rate under periodic driving decays exponentially with an increase in driving frequency. This result is applicable across different spatial dimensions, which implies a strong dependence of heating dynamics on the driving frequency. This challenges prior ideas about unavoidable heating at high frequencies in Floquet systems.
2. Local vs. Global Driving: The paper differentiates between local and global driving cases. Local driving pertains to systems where the periodic driving perturbation affects only a finite number of lattice sites. In contrast, global driving involves perturbation applied uniformly across the entire system. The authors establish rigorous bounds for both cases, showing how the nature and intensity of driving impact the energy absorption rates.
3. Implications for Floquet Many-Body Phases: An important implication of the paper is the potential stability of Floquet many-body phases even though they are inherently metastable due to periodic driving breaking energy conservation. The results provide a theoretical foundation for the experimental realization of long-lived Floquet states given sufficiently high driving frequencies.
4. Mathematical Framework and Bounds: The authors employ advanced mathematical frameworks, including Lieb-Robinson bounds, to derive the energy absorption estimates. They show that these bounds ensure the dissipative part of the response function decays exponentially. This mathematical rigor helps in confirming the robustness of the results across many-body systems lacking energy gaps or systems with strong interactions.

Discussion and Implications

The results presented have significant implications for the paper of many-body quantum systems under periodic driving, particularly in the context of Floquet engineering. The finding that heating can be suppressed exponentially through high-frequency drives enhances our understanding of floquet topological insulators and other many-body systems’ dynamic localization properties. For experimental physicists, this work suggests practical guidelines for minimizing heating in quantum systems, facilitating more controlled and efficient implementations of quantum technologies.

Moreover, the paper's findings align with phenomena observed in cold atomic systems and serve as a theoretical guidepost for experiments aiming to explore fractional topological states and symmetry-protected topological order in driven systems. The suggested extension beyond linear response frameworks to consider general initial states hints at similarities with energy localization phenomena, thus opening new lines of research in exploring long-term dynamics in driven systems.

Future Directions

While the paper provides substantial insight into periodically driven systems' dynamic responses, numerous avenues remain for future exploration. Further studies could extend these ideas into non-linear regimes or explore systems with more complex interaction structures. Another potential research direction is the application of these concepts in the context of quantum computing and advanced material design, where controlling heating and energy dissipation is crucial. Additionally, investigating the impact of disorder and randomness in periodically driven systems may yield deeper understanding and control over quantum coherence in practical applications.