Functional relations and the Yang-Baxter algebra

Abstract

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.

23 pages. Contribution to the proceedings of the ISQS21

References in corpus (2)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• SOS model partition function and the elliptic weight functions

Cited by in corpus (7)

• Reflection algebra and functional equations
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Twisted Heisenberg chain and the six-vertex model with DWBC
• Integral formula for elliptic SOS models with domain walls and a reflecting end
• Partial differential equations from integrable vertex models
• New differential equations in the six-vertex model
• Continuous representations of scalar products of Bethe vectors