Ground-state properties of the spin-1/2 Heisenberg-Ising bond   alternating chain with Dzyaloshinskii-Moriya interaction
  Ground-state energy is exactly calculated for the spin-1/2 Heisenberg-Ising bond alternating chain with the Dzyaloshinskii-Moriya interaction. Under certain condition, which relates a strength of the Ising, Heisenberg and Dzyaloshinskii-Moriya interactions, the ground-state energy exhibits an interesting nonanalytic behavior accompanied with a gapless excitation spectrum. 
J. Strecka, L. Galisova, O. Derzhko
cond-mat.stat-mech