I would like to know the analytical expression of the ground state energy of the XXZ model, if such formula exists (probably from a Bethe Ansatz solution) and if it is valid in all parameter regimes.
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Such analytical expressions were derived for special cases by multiple authors. More general results were obtained by Yang and Yang in
For example, the ground state energy for zero magnetization is specifically addressed in Eqs. (31a-d), and later simplifications in the paper. There, the symbol $f(\Delta,y)$ is used to denote ground state energy at net magnetization $y$. This notation is introduced in the preceding paper, C. N. Yang and C. P. Yang, Phys. Rev. 150, 321 (1966), which is a better starting point for reading than part II. Further, some additional useful results were given in the slightly earlier paper C. N. Yang and C. P. Yang, Phys. Rev. 147, 303 (1966).
