Critical and off-critical properties of the XXZ chain in external homogeneous and staggered magnetic fields

The phase diagram of the XXZ chain under the influence of homogeneous and staggered magnetic fields is calculated. 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 has its critical fluctuations governed by a conformal field theory with central charge c = 1. When the σ-anisotropy ∆ is zero the model is exactly integrable through a JordanWigner fermionization and our results are analytic. For ∆ 6= 0 our analysis are done numerically using lattice sizes up to M = 20. Our results shows that for −1 ≥ ∆ ≥ √ 2 2 the staggered magnetic field perturbation is relevant and for 1 ≤ ∆ ≤ √ 2 2 it is irrelevant. In the region of relevant perturbations we show that the massive continuum field theory associated to the model has the same mass spectrum as the sine-Gordon model.