Thermalization slowing down of weakly nonintegrable quantum spin dynamics

Summary

The study investigates thermalization slowing down in weakly nonintegrable quantum spin dynamics, focusing on two distinct integrability limits. It identifies two thermalization time scales: one from the quantum Lyapunov time scale and another from the ergodization time scale related to the eigenstate thermalization hypothesis.

Highlights

• The study explores thermalization slowing down in quantum many-body spin systems near integrability.
• Two thermalization time scales are identified: quantum Lyapunov time and ergodization time.
• The quantum Lyapunov time scale is extracted by quantifying operator growth in time.
• Ergodization time is related to the statistics of fluctuations of the time-evolved operator around its mean value.
• The study uses a paradigmatic Quantum Ising chain to investigate these time scales.
• Both time scales diverge upon approach to integrability, with similar fashion despite qualitative differences in integrability breaking mechanisms.
• The results establish a universality of integrability breaking in quantum spin dynamics.

Key Insights

• The study demonstrates that thermalization slowing down is a universal property of non-integrable systems, applicable to both classical and quantum dynamics.
• The quantum Lyapunov time scale, related to operator growth, provides a new perspective on thermalization, distinct from traditional measures like the Lyapunov exponent.
• Ergodization time, derived from the eigenstate thermalization hypothesis, captures the statistical properties of time-evolved operators, offering insights into the thermalization process.
• The similar divergence behavior of both time scales near integrability suggests a deep connection between operator growth and thermalization in quantum systems.
• The universality of integrability breaking in quantum spin dynamics, as revealed by the study, has implications for understanding the behavior of quantum systems across different regimes.
• The study's findings have potential applications in the study of quantum many-body systems, quantum chaos, and the development of new quantum technologies.
• The use of a paradigmatic Quantum Ising chain as a model system allows for a detailed exploration of thermalization dynamics, providing a foundation for future studies in more complex systems.

Mindmap

Citation

Bhattacharjee, B., Andreanov, A., & Flach, S. (2024). Thermalization slowing down of weakly nonintegrable quantum spin dynamics (Version 3). arXiv. https://doi.org/10.48550/ARXIV.2405.00786