The Bethe Ansatz

Trigonometric \(R\)-matrix and the XXZ chain debab.Slavnov2018-5

  • Slavnov2018-5-1.1

\[ \left( \begin{array}{cccc} f(u,v) & 0 & 0 & 0 \\ 0 & 1 & g(u,v) & 0 \\ 0 & g(u,v) & 1 & 0 \\ 0 & 0 & 0 & f(u,v) \end{array} \right) \]

  • Slavnov2018-5-1.2

\[ f(u,v) = \frac{\sinh(u-v+\eta)}{\sinh(u-v)}, \hspace{10mm} g(u,v) = \frac{\sinh(\eta)}{\sinh(u-v)} \]

  • Slavnov2018-5-1.6

\[ L_n(u) = \left( \begin{array}{cc} \sinh(u + \frac{\eta}{2} \sigma^z_n) & \sigma^-_n \sinh \eta \\ \sigma^+ \sinh \eta & \sinh(u - \frac{\eta}{2} \sigma^z_n) \end{array} \right) \]




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Author: Jean-Sébastien Caux

Created: 2026-08-26 Wed 11:07