{getToc} $title={Table of Contents}
Summary
The study investigates quantum spin transport in a one-dimensional folded XXZ model using the Bethe ansatz technique, finding that the probability distribution of the left-most up-spin converges to the Tracy-Widom distribution for the Gaussian unitary ensemble (GUE) in the long-time limit.
Highlights
- The study examines quantum spin transport in the one-dimensional folded XXZ model.
- The Bethe ansatz technique is used to derive an exact expression for the probability distribution of the left-most up-spin.
- The probability distribution is found to converge to the GUE Tracy-Widom distribution in the long-time limit.
- The GUE Tracy-Widom distribution is a universal distribution that appears in various physical systems.
- The study's findings suggest that the folded XXZ model exhibits similar behavior to other integrable models.
- The results have implications for understanding the behavior of interacting quantum systems.
- The study provides a new example of the GUE Tracy-Widom distribution in a quantum system.
Key Insights
- The folded XXZ model is an integrable model that can be solved using the Bethe ansatz technique, allowing for an exact derivation of the probability distribution of the left-most up-spin.
- The convergence of the probability distribution to the GUE Tracy-Widom distribution in the long-time limit suggests that the folded XXZ model exhibits universal behavior similar to other integrable models.
- The GUE Tracy-Widom distribution is a probability distribution that appears in various physical systems, including random matrix theory and the Kardar-Parisi-Zhang (KPZ) universality class.
- The study's findings have implications for understanding the behavior of interacting quantum systems, particularly in the context of quantum transport and the emergence of universal behavior.
- The use of the Bethe ansatz technique and the derivation of an exact expression for the probability distribution demonstrate the power of integrability in solving complex quantum systems.
- The study provides a new example of the GUE Tracy-Widom distribution in a quantum system, expanding our understanding of the universality of this distribution.
- The results of the study suggest that the folded XXZ model may be a useful system for exploring the behavior of interacting quantum systems and the emergence of universal behavior.
Mindmap
If MindMap doesn't load, go to the Homepage and visit blog again or Switch to Android App (Under Development).
Citation
Fujimoto, K., & Sasamoto, T. (2024). Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20147