Spin-wave gap critical index for the quantum two-layer heisenberg antiferromagnet at T = 0

The two-layer Heisenberg antiferromagnet exhibits a zero temperature quantum phase transition from a disordered dimer phase to a collinear Neel phase, with long range order in the ground state. The spin-wave gap vanishes as Δ ∝ (J_⊥ -J_⊥c)^ν approaching the transition point. To account for strong correlations, the S = 1 elementary excitations triplets are described as a dilute Bose gas with infinite on-site repulsion. We apply the Brueckner diagram approach which gives the critical index ν ≈ 0.5. We demonstrate also that the linearised in density Brueckner equations give the mean field result ν = 1. Finally, an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, gives ν ≈ 0.67. This value agrees reasonably with that of the nonlinear O(3) σ model. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear σ model. We discuss the conditions for this to occur.