CRITICAL AND OFF-CRITICAL PROPERTIES OF THE XXZ CHAIN IN EXTERNAL HOMOGENEOUS AND STAGGERED MAGNETIC-FIELDS

The phase diagram of the XXZ chain is calculated under the influence of homogeneous and staggered magnetic fields. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase's critical fluctuations are governed by a conformal field theory with central charge c = 1. When the sigma(z)-anisotropy Delta is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For Delta not equal 0 our analysis is done numerically using lattice sizes up to M = 20. Our results show that for -1 less than or equal to Delta < root 2/2 the staggered magnetic field perturbation is relevant, whereas for root 2/2 < Delta less than or equal to 1 it is irrelevant. In the region of relevant perturbations, we show that the massive continuum field theory associated with the model, has the same mass spectrum as the sine-Gordon model.