By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of sqrt[2] to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. Its width is observed to vanish proportional to the Higgs mass in the accessible proximity to the quantum critical point.By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of sqrt[2] to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. Its width is observed to vanish proportional to the Higgs mass in the accessible proximity to the quantum critical point.

arXiv:1610.05063Physical Review LettersApr 6, 201723 citations

Quantum criticality and universal scaling of a quantum antiferromagnet

B. Lake, D. M. Tennant, Chris D. Frost +1 more

arXiv:cond-mat/0501069Nature MaterialsMar 20, 2005340 citations

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

Pavel V. Shevchenko, Oleg P. Sushkov

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.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.

arXiv:cond-mat/9809368Physical review. B, Condensed matterApr 1, 199910 citations

Quantum and Classical Criticality in a Dimerized Quantum Antiferromagnet

Christian Rüegg, Philip Merchant, MCMORROW Desmond Francis +3 more

Bulletin of the American Physical SocietyMar 7, 20140 citations

Cubic Interactions and Quantum Criticality in Dimerized Antiferromagnets

Stefan Weßel, Lars Fritz, R. L. Doretto +3 more

Bulletin of the American Physical SocietyFeb 29, 20120 citations

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.