Université de Fribourg

The Bethe Ansatz for the six-vertex and XXZ models: An exposition

Duminil-Copin, Hugo ; Gagnebin, Maxime ; Harel, Matan ; Manolescu, Ioan ; Tassion, Vincent

In: Probability Surveys, 2018, vol. 15, p. 102–130

In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector ψ and energy Λ, which satisfy Vψ=Λψ, where V is the transfer matrix of the six-vertex model on a finite square lattice with periodic boundary conditions for weights a=b=1 and c>0. We also show that the same vector ψ satisfies Hψ=Eψ, where H is the...