Theory of the Néel and collinear phases in the J1-J2 model of a spin-1/2 square-lattice frustrated antiferromagnet.

Abstract

We present a perturbation scheme for evaluating the ground-state characteristics of N\'eel and collinear phases of the spin-1/2 ${\mathrm{J}}_{1\mathrm{\ensuremath{-}}}$${\mathit{J}}_{2}$ model. Using the Dyson-Maleev formalism and performing a canonical transformation to exclude strong interaction between bosons, we convert the Hamiltonian of the ${\mathit{J}}_{1\mathrm{\ensuremath{-}}}$${\mathit{J}}_{2}$ model to the Hamiltonian ${\mathit{H}}_{\mathrm{DM}}$=${\mathit{H}}_{0}$+${\mathit{V}}_{\mathrm{DM}}$, where ${\mathit{H}}_{0}$ represents a noninteracting gas of quasiparticles and ${\mathit{V}}_{\mathrm{DM}}$ is a normal-ordered quartic operator. The description, based on the zero-order Hamiltonian ${\mathit{H}}_{0}$, turns out to be equivalent to the description of ordered phases, obtained earlier in the framework of modified spin-wave theory (MSWT). We carry out perturbation-type calculations up to second order in ${\mathit{V}}_{\mathrm{DM}}$ for the ground-state energy and magnetization and obtain small corrections in a wide range of the frustration parameter \ensuremath{\alpha} (=${\mathit{J}}_{\mathit{z}}$/${\mathit{J}}_{1}$). It is shown that near the phase boundaries the spin-wave interaction causes an essential melting effect. The corrected value of magnetization of the N\'eel (collinear) phase goes to zero at \ensuremath{\alpha}\ensuremath{\simeq}0.52 (\ensuremath{\alpha}\ensuremath{\simeq}0.57). Thus, within a second-order approximation a window 0.520.57 instead of the MSWT overlap between N\'eel and collinear phases is found.