Invitation to the Bethe ansatz
Reiho Sakamoto
TL;DR
This paper reviews the algebraic Bethe ansatz for the Heisenberg model, explores recent advancements, and discusses connections with rigged configurations, crystal bases, and the inverse scattering transform for certain integrable systems.
Contribution
It offers a comprehensive review of the algebraic Bethe ansatz, recent developments, and reformulates key results related to rigged configurations and crystal bases.
Findings
Provides the inverse scattering transform for type D^{(1)}_n box-ball systems
Reformulates a significant result from arXiv:0711.4185
Highlights the relation between Bethe ansatz and rigged configurations
Abstract
We review the algebraic Bethe ansatz for the Heisenberg model. The exposition includes some of recent advancements with emphasis on a relation with the rigged configurations. We also provide somewhat thorough review of the crystal bases and the rigged configurations. In particular, we provide the inverse scattering transform for the type box-ball systems. We also provide a reformulation of a result of arXiv:0711.4185.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Advanced Algebra and Geometry