Abstracts

Igor Salom

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain

We will start with an introduction to the Algebraic Bethe Ansatz. Considering the periodic case of the XXX Heisenberg spin chain, we will introduce the notions of R-matrices, Lax operator, monodromy, transfer matrix, Bethe equations, etc. Then we will consider the actual problem of the XXZ spin chain with non-periodic boundary conditions. We will show our results for the corresponding Bethe vectors and explicitly write transfer matrix action on these vectors in the off-shell form. Furthermore, we will discuss certain degrees of freedom for the choice of off-shell solutions, which systematically appear in this context.