TheA⁽²⁾₂Gaudin model and its associated Knizhnik–Zamolodchikov equation

Abstract

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted A (2) 2 R-matrix. We find the spectra and eigenvectors of the N − 1 independents Gaudin Hamiltonians . We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.

Integrable time-dependent Hamiltonians, solvable Landau–Zener models and Gaudin magnets

“…where we used the second equation in (40) and the last two equations in (42). By construction Ψ D (t, ξ) also satisfies the remaining (j = 1, .…”

“…Naturally, by definition we include in the Gaudin-KZ class other integrable versions of Gaudin magnets and corresponding KZ equations, such as trigonometric, hyperbolic, generalized to other Lie algebras instead of spin su(2) etc. [17,19,[38][39][40][41][42].…”

osp(1|2) off-shell Bethe ansatz equation with boundary terms

“…[23]. In a series of papers [24,25,26] we have considered the 19-vertices models, the osp(1|2) model and the twisted A or Izergin-Korepin model and the sl(2|1) (2) model, respectively. In these works, the OSBAE procedure was used in order to find and solve the corresponding Gaudin models, as well as, the corresponding KZ equations.…”

“…B 1 b 3 = d 11 b 3 B 1 + d 12 b 1 B 1 + d 13 b 2 D 1 + d 14 b 2 D 2 + b 15 B 2 d 1 + d 16 B 2 d 2 + d 17 B 2 d D 11 c 1 C 3 + D 12 c 1 C 1 + D 13 d 1 C 2 + D 14 d 2 C 2 + D 15 D 1 c 2 + D 16 D 2 c 2 + D 17 D 3 c 2 (A 25). …”

Modelos de emparelhamento integráveis

“…Este método que faz uso da matriz de transferência e seus operadores A(u) e D(u) é conhecido na literatura como o ansatz de Bethe algébrico (ABA) [6,7,8] e corresponde ao cerne desta dissertação, uma vez que é a técnica matemática que aplicaremos em todos os modelos de spins estudados nos capítulos seguintes.…”