Bilayer Heisenberg model studied by the Schwinger-boson Gutzwiller-projection method

A two-dimensional, bilayer, square lattice Heisenberg model with different intraplane (${\mathit{J}}_{\mathrm{\parallel }}$) and interplane(${\mathit{J}}_{\mathrm{\perp }}$) couplings is investigated. The model is first solved in the Schwinger-boson mean-field approximation. Then the solution is Gutzwiller projected to satisfy the local constraint that there should be only one boson at each site. For these wave functions, we perform variational Monte Carlo simulation up to 24×24×2 sites. It is shown that the Néel order is destroyed as the interplane coupling is increased. The obtained critical value, ${\mathit{J}}_{\mathrm{\perp }}$/${\mathit{J}}_{\mathrm{\parallel }}$=3.51, is smaller than that obtained by the mean-field theory. The excitation spectrum is calculated by a single-mode approximation. It is shown that the energy gap develops once the Néel order is destroyed. © 1996 The American Physical Society.