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arXiv:cond-mat/9809368 · Physical review. B, Condensed matter

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

Pavel V. Shevchenko, Oleg P. Sushkov

Published Apr 1, 1999• 10 citations
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Abstract

We consider the two-layer Heisenberg antiferromagnet near a zero-temperature quantum phase transition from a disordered dimer phase to a N\'eel state. At approaching the transition point the spin-wave gap vanishes as $\ensuremath{\Delta}\ensuremath{\propto}{(J}_{\ensuremath{\perp}}\ensuremath{-}{J}_{\ensuremath{\perp}c}{)}^{\ensuremath{\nu}}.$ To account for strong correlations between the $S=1$ elementary excitations we apply the Brueckner diagram approach which gives the critical index $\ensuremath{\nu}\ensuremath{\approx}0.5.$ We demonstrate also that the linearized in density Brueckner equations give the mean field result $\ensuremath{\nu}=1.$ Finally an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, give $\ensuremath{\nu}\ensuremath{\approx}0.67.$ This value reasonably agrees with that of the nonlinear $O(3) \ensuremath{\sigma} \mathrm{model}.$ Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear $\ensuremath{\sigma}$ model. We discuss the conditions for this to occur.

DOI
10.1103/physrevb.59.8383

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We consider the two-layer Heisenberg antiferromagnet near a zero-temperature quantum phase transition from a disordered dimer phase to a N'eel state. At approaching the transition point the spin-wave gap vanishes as \ensuremathΔ\ensuremath∝(J\ensuremath⊥\ensuremath−J\ensuremath⊥c)\ensuremathν.\ensuremath{\Delta}\ensuremath{\propto}{(J}_{\ensuremath{\perp}}\ensuremath{-}{J}_{\ensuremath{\perp}c}{)}^{\ensuremath{\nu}}.\ensuremathΔ\ensuremath∝(J\ensuremath⊥​\ensuremath−J\ensuremath⊥c​)\ensuremathν. To account for strong correlations between the S=1S=1S=1 elementary excitations we apply the Brueckner diagram approach which gives the critical index \ensuremathν\ensuremath≈0.5.\ensuremath{\nu}\ensuremath{\approx}0.5.\ensuremathν\ensuremath≈0.5. We demonstrate also that the linearized in density Brueckner equations give the mean field result \ensuremathν=1.\ensuremath{\nu}=1.\ensuremathν=1. Finally an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, give \ensuremathν\ensuremath≈0.67.\ensuremath{\nu}\ensuremath{\approx}0.67.\ensuremathν\ensuremath≈0.67. This value reasonably agrees with that of the nonlinear O(3)\ensuremathσmodel.O(3) \ensuremath{\sigma} \mathrm{model}.O(3)\ensuremathσmodel. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear \ensuremathσ\ensuremath{\sigma}\ensuremathσ model. We discuss the conditions for this to occur.
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