Nested Algebraic Bethe Ansatz in integrable models: recent results

TL;DR

This paper reviews recent advances in the nested algebraic Bethe ansatz for integrable models, focusing on the construction of Bethe vectors, scalar products, and form factors for models based on (super)algebras.

Contribution

It summarizes new methods for constructing Bethe vectors and calculating scalar products and form factors in integrable models with (super)algebra symmetries.

Findings

Construction of Bethe vectors for various (super)algebras.

Explicit formulas for scalar products and form factors.

Application to models based on $gl_n$, $gl_{m|p}$, and their quantum deformations.

Abstract

This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A. Hutsalyuk (Wuppertal / Moscow) and A. Liashyk (Kiev / Moscow). It presents the construction of Bethe vectors, their scalar products and the form factors of local operator for integrable models based on the (super)algebras $gl_n$, $gl_{m|p}$ or their quantum deformations. It corresponds to two talks given by E.R. and N.S. at \textsl{Correlation functions of quantum integrable systems and beyond}, in honor of Jean-Michel Maillet for his 60's (ENS Lyon, October 2017).