Abstract
Abstract We have investigated the S= 1 2 alternating anti-ferromagnetic Heisenberg chain (AHC) and the XXZ chain using the bosonization and Lanczos methods. For the AHC, the asymptotic behavior of the ground state energy per site is obtained and a new finite size scaling procedure is proposed to extrapolate the energy gap to bulk limit. The results show a good agreement with the theoretical prediction, especially for the dependence of the energy gap on the dimerization parameter, the 2 3 power law with logarithmic correction anticipated by the renormalization group theory is confirmed. We also calculate the scaling dimensions of various operators in the XXZ chain for different anisotropic parameters Δ(0⩽Δ⩽1).
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