Low-energy properties of anisotropic two-dimensional spin- 1 2 Heisenberg models in staggered magnetic fields

Bin Xi1,2,3Shijie Hu4,1Jize Zhao5,6Gang Su3B. Normand1, and Xiaoqun Wang1

  • 1Department of Physics, Renmin University of China, Beijing 100872, China
  • 2Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 3College of Physical Sciences, Graduate University of the Chinese Academy of Sciences, Beijing 100049, China
  • 4Institut für Theoretische Physik, Georg-August-Universität Goettingen, D-37077 Göttingen, Germany
  • 5Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
  • 6Department of Physics and Astronomy, California State University, Northridge, California 91330, USA


We present a systematic study of the anisotropic spin-1/2 Heisenberg model in staggered magnetic fields in two dimensions. To mimic real materials, we consider a system of coupled, antiferromagnetic chains, whose interchain interaction can be either ferro- or antiferromagnetic. When the staggered field is commensurate with the magnetic interactions, an energy gap opens immediately and follows a power law as a function of the applied field, similar to the situation in one dimension. When the field competes with the interactions, a quantum phase transition (QPT) occurs from a gapless, magnetically ordered phase at low fields to a gapped, disordered regime. We use a continuous-time Monte Carlo method to compute the staggered moment of the ordered phases and the spin gap of the disordered phases. We deduce the phase diagrams as functions of the anisotropy ratio and the applied field, and calculate the scaling behavior of the models in both quantities. We show that in the competitive case, the staggered field acts to maintain a regime of quasi-1D behavior around the QPT, and we discuss as a consequence the nature of the crossover from one-dimensional (1D) to 2D physics.

  • Received 23 June 2011


©2011 American Physical Society