
%0 Journal Article
%A Shevchenko, P. V. 
%A Sushkov, O. P. 
%T Spin-wave Gap Critical Index for the Quantum Two-layer Heisenberg Antiferromagnet at <emph type="2">T</emph> = 0
%J Australian Journal of Physics
%D 1999/08/27
%V 52
%N 5
%P 837-844
%K 
%R https://doi.org/10.1071/PH98099
%U https://www.publish.csiro.au/paper/PH98099 
%X 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 &#916; &prop; (J &perp; &#8211; J &perp; c) &ngr; 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 &ngr; &#x2248; 0 . 5. We demonstrate also that the linearised in density Brueckner equations give the mean field result &ngr; = 1. Finally, an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, gives &ngr; &#x2248; 0 . 67. This value agrees reasonably with that of the nonlinear O(3) &#963; model. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear &#963; model. We discuss the conditions for this to occur. 
