Renormalization-group studies of antiferromagnetic chains. I. Nearest-neighbor interactions

Abstract

The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation, a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformation can be defined for models other than those considered here, and may be useful in various block-spin calculations.