CHERN-SIMONS THEORY OF THE ANISOTROPIC QUANTUM HEISENBERG-ANTIFERROMAGNET ON A SQUARE LATTICE

Article

关键词: LONG-RANGE ORDER;    2 DIMENSIONS;    FIELD-THEORY;    FRACTIONAL-STATISTICS;    WAVE-FUNCTIONS;    CRITICAL EXPONENTS;    PHASE-TRANSITIONS;    TOPOLOGICAL TERMS;    SYMMETRY BREAKING;    SPIN SYSTEMS;   

DOI  :  10.1103/PhysRevB.49.15139

来源: SCIE

【 摘 要 】

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

【 授权许可】

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