Quantum phase transitions in a spin-1/2 alternating Heisenberg   antiferromagnetic chain under a staggered transverse magnetic field
  The magnetic behaviors of a spin-1/2 alternating Heisenberg antiferromagnetic chain in a staggered transverse magnetic field is studied by means of the density-matrix renormalization group method and Jordan-Wigner transformation. Quantum phase transitions of different types are observed in the S=1 Neel and XY-like gapless phases, which result from the competitions between the staggered transverse field and magnetic orders induced by anisotropy and alternating interactions. The results are compared with the mean-field and some exactly resolved results. 
Guang-Qiang Zhong, Shou-Shu Gong, Qing-Rong Zheng, Gang Su