Nonlinearσmodels for triangular quantum antiferromagnets

Abstract

We expand the long-wavelength action of two-dimensional quantum Heisenberg antiferromagnets on a triangular lattice around the Néel-ordered classical ground state and map it onto a nonlinear σ model, where the field is an SO(3) element, describing the local orientation of the magnetizations on the three sublattices. No topological information on the microscopic value of the spin S is seen to subsist in the mapping, although some nontrivial third-order terms are found.