Bond-operator approach to the bilayer Heisenberg antiferromagnet

Abstract

The bilayer spin-$1/2$ antiferromagnetic Heisenberg model is studied by the bond-operator mean-field theory and perturbation theory. From both methods, the zero-temperature quantum phase transition occurs at a critical ratio of ${(J}_{2}{/J}_{1}{)}_{c}\ensuremath{\approx}2.3,$ where ${J}_{1}$ and ${J}_{2}$ are the intralayer and interlayer coupling constants. Under the mean-field method, the obtained spin-wave mass, uniform susceptibility, and inverse correlation length at the critical point show good linear behavior versus temperature at low temperatures, in agreement with results of the nonlinear $\ensuremath{\sigma}$ model and quantum Monte Carlo simulations. On the other hand, the finite temperature perturbation theory gives a good description of the disordered phase in quite a large temperature range. The specific heat and uniform susceptibility exhibit broad maxima versus temperature, consistent with series expansion results.