SU(2) Coherent State Path Integral Formulation of Nonlinear Collective Modes of Magnons in Heisenberg Antiferromagnets —Self-Localized Magnons and Vortices—

Abstract

A path integral theory in the SU(2) coherent state representation of elementary excitations in Heisenberg antiferromagnets is developed, in which no assumption is made on the smallness of spin deviations from the Néel state. Use of the stationary phase approximation leads to the Lagrangian equations in which the nonlinearity intrinsic to the magnon system is fully included at the cost of neglecting quantum fluctuations in the coherent state basis. Full nonlinear equations so obtained are of a simple renormalized form in the boson coherent state path integral formulation using the Dyson-Maleev transformation. The formal theory is illustrated to show the existence under certain conditions of self-localized magnons below the linear magnon energy band and of vortex-like modes in two-dimensional cases.