Functional relations and the Yang-Baxter algebra

21st International Conference on Integrable Systems and Quantum Symmetries

Galleas, Wellington^1

Institute for Theoretical Physics, Spinoza Institute, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, Netherlands^1

关键词: Exactly solvable model;    Functional equation;    Functional relation;    Integrable systems;    Partition functions;    Transfer matrixes;    Wall boundaries;    Yang-Baxter equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012020/pdf
DOI  :  10.1088/1742-6596/474/1/012020

来源: IOP

【 摘 要 】

Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the celebrated Yang-Baxter equation which plays a fundamental role for the construction of quantum integrable systems and also for obtaining their exact solution. Here I shall discuss a proposal that has been put forward in the past years, in which the Yang-Baxter algebra is viewed as a source of functional equations describing quantities of physical interest. For instance, this method has been successfully applied for the description of the spectrum of open spin chains, partition functions of elliptic models with domain wall boundaries and scalar product of Bethe vectors. Further applications of this method are also discussed.