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-temperatur e quantum phase transition from a disordered dimer phase to a Neel state. A t approaching the transition point the spin-wave gap vanishes as Delta prop ortional to (J(perpendicular to) -J(perpendicular to c))(v). To account for strong correlations between the S = 1 elementary excitations we apply the Brueckner diagram approach which gives the critical index v approximate to 0.5. We demonstrate also that the linearized in density Brueckner equations give the mean field result v = 1. Finally an expansion of the Brueckner eq uations in powers of the density, combined with the scaling hypothesis, giv e v approximate to 0.67. This value reasonably agrees with that of the nonl inear O(3) sigma model. Our approach demonstrates that for other quantum sp in models the critical index can be different from that in the nonlinear si gma model. We discuss the conditions for this to occur. [S0163-1829(99)0121 0-2].