The magnetoelastic mechanism of singlet phase formation in a two-dimensional quantum antiferromagnet

A model describing the second-order phase transition with respect to the magnetoelastic coupling parameter from the antiferromagnetic (AFM) to the singlet state in a two-dimensional quantum magnet on a square lattice is proposed. The spectrum of elementary excitations in the singlet and AFM phases is calculated using an atomic representation, and the evolution of transverse and longitudinal branches of this spectrum is studied in the vicinity of the transition point. It is established that the AFM to singlet phase transition is related to softening of the longitudinal branch of oscillations. In the singlet phase, the gap plays the role of a parameter characterizing the distance to the phase transition point. It is shown that the spectrum of transverse oscillations in the AFM phase corresponds to the Goldstone boson. Based on an analysis of the stability of the spectrum of elementary excitations, a phase diagram is constructed that determines the regions of the existence of phases with plaquette-deformed lattices. © Pleiades Publishing, Inc., 2006.