Brueckner approach to the spin-wave gap critical index for the two-layer Heisenberg antiferromagnet

We consider the two-layer Heisenberg antiferromagnet near a zero-temperature quantum phase transition from a disordered dimer phase to a Néel state. At approaching the transition point the spin-wave gap vanishes as Δ∝(J_⊥-J_⊥c)^v. To account for strong correlations between the S= 1 elementary excitations we apply the Brueckner diagram approach which gives the critical index vπ0.5. We demonstrate also that the linearized in density Brueckner equations give the mean field result v= 1. Finally an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, give v≈0.67. This value reasonably agrees 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.