The spin-1/2 anisotropic Heisenberg-chain in longitudinal and   transversal magnetic fields: a DMRG study
  Using the density matrix renormalization group technique, we evaluate the low-energy spectrum (ground state and first excited states) of the anisotropic antiferromagnetic spin-one-half chain under magnetic fields. We study both homogeneous longitudinal and transversal fields as well as the influence of a transversal staggered field on opening of a spin-gap. We find that only a staggered transversal field opens a substantial gap. 
F. Capraro, C. Gros