Chern-Simons theory of the anisotropic quantum Heisenberg antiferromagnet on a square lattice.

摘要: We consider the anisotropic quantum Heisenberg antiferromagnetic (with anistropy [lambda]) on a square lattice using Chern-Simons (or Wigner-Jordan) approach. show that average field approximation (AFA) yields phase diagram with two phases: Neel state for [lambda][gt][lambda][sub [ital c]] and flux [lambda][lt][lambda][sub separated by second-order transition at [lambda][sub c]][lt]1. this does not describe XY] regime of antiferromagnet. Fluctuations around AFA induce relevant operators which yield correct diagram. find an equivalence between antiferromagnet relativistic theory self-interacting Dirac fermions coupled to gauge field. The has number Goldstone modes in each critical coupling [lambda][sup *][gt][lambda][sub c]]. identify isotropic point. It nonvanishing order parameter, drops zero discontinuously [lambda][lt][lambda][sup *].