Critical behavior of anisotropic spin-SHeisenberg chains

Using a Lanczos method, we study the spectra of Heisenberg chains with spin S=1, 3/2, 2, 5/2, and 3, as a function of the anisotropy parameter λ and the number of sites of the chain. We use periodic, twisted, and open boundary conditions. We found that for all values of the spin when -1≤λ≤0, these models are massless with critical behavior described by a conformal theory with central charge c=1. We discuss the whole operator content. In particular, we found that the critical exponent ${\mathrm{\eta }}_{\mathit{x}}$ follows the behavior ${\mathrm{\eta }}_{\mathit{x}}$=(π-γ)/2πS and ${\mathrm{\eta }}_{\mathit{z}}$=2 where γ=${\cos }^{\mathrm{-}1}$(λ). For λ>0, our results indicate that the S=1 model is massive, while for S>1, the massless behavior characterized by the critical exponents described above continues up to λ=${\lambda }^{\mathrm{*}}$(S). For ${\lambda }^{\mathrm{*}}$<λ≤1, our results are consistent with a massive phase for the integer-spin models and a massless phase with a rapid variation of the critical exponents for the half-integer-spin models.