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

Abstract

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=0 our analysis is done numerically using lattice sizes up to M=20. Our results show that for -1<or= Delta < square root (2/2) the staggered magnetic field perturbation is relevant, whereas for square root (2/2)< Delta <or=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.