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Semiclassical action of two-dimensional spin-12 Heisenberg antiferromagnet

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  • Holz, A.

Abstract

A semiclassical action (Гsc) of the spin-12 Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is derived using unitary transformations to noninertial and nonuniform coordinate- and Hilbert space frames, based on a recently developed gauge theory of the spin-12 HA. The effective action is derived using field theoretic zero temperature perturbation theory, based on regular Néel sublattices and has the structure of an anisotropic σ model, whose dynamic variables are the three Maurer-Cartan 1-forms of the SO(3) group space. Potential terms in Γsc, being of second order in spatial derivatives, carry a negative sign and suggest that regular Néel sublattices are unstable. In perturbation theory no topological invariant of Hopf's or Wess-Zumino type enters Γsc, but phase factors of Berry's type do. Infrared infinities in some of the coefficients of Γsc suggest that nonperturbative methods may have to be used and lead to structural changes of Γsc.

Suggested Citation

  • Holz, A., 1991. "Semiclassical action of two-dimensional spin-12 Heisenberg antiferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 170(3), pages 543-570.
    • Handle: RePEc:eee:phsmap:v:170:y:1991:i:3:p:543-570
    DOI: 10.1016/0378-4371(91)90006-X
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