Bi-layer Heisenberg model studied by the Schwinger-boson Gutzwiller-projection method

A two-dimensional bi-layer, square lattice Heisenberg model with different intraplane($J_{\parallel}$) and interplane($J_{\perp}$) couplings is investigated. The model is first solved in the Schwinger boson mean-field approximation. %It is shown that order-disorder transition occurs as the interplane Coupling %is increased. The critical ratio is J_{\perp/\p=4.48J 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 $24 \times 24 \times 2$ sites. It is shown that the N\'eel order is destroyed as the interplane coupling is increased. The obtained critical value, $J_{\perp}/J_{\parallel}=3.51$, is smaller than that by the mean-field theory. Excitation spectrum is calculated by a single mode approximation. It is shown that energy gap develops once the N\'eel order is destroyed.