Algebraic analysis of strongly correlated systems (No. 09.3.3-LMT-K-712-02-0017)

Models of strongly correlated systems constitute an important class of integrable models and are widely used in both physics and mathematics. Such models are used to describe electronic theory and thermodynamic properties of solid state bodies, phase transitions in superconductors, stochastic processes and Markov chains. This project will focus on the spectral problem of strongly correlated systems that exhibit orthogonal and symplectic Yangian symmetries and have open boundary conditions. The spectral problem will be approached by means of the highest-weight theory and the nested algebraic Bethe anstaz. The main goal is to construct Bethe vectors and find nested Bethe equations, the roots of which describe the spectrum of the physical states in the model. This is the most important first step in the study of such models. They key challenge is to find a well-suited algebraic description allowing the implementation of the nesting procedure for the fundamental and spinor representations. Overcoming these challenges will also help to better understand representation theory of twisted Yangians for orthogonal and symplectic Lie algebras.

Research fellow: dr. Vidas Regelskis
Fellowship supervisor: dr. Artūras Acus