Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

TL;DR

This study uses large-scale quantum Monte Carlo simulations to analyze the quantum critical scaling of the excitation gap in a 3D antiferromagnet, revealing logarithmic corrections and identifying the Higgs mode resonance consistent with field theory predictions.

Contribution

It provides the first detailed numerical verification of logarithmic scaling corrections and Higgs mode behavior in a three-dimensional quantum antiferromagnet near criticality.

Findings

Logarithmic scaling corrections to the excitation gap near criticality.

Identification of the Higgs mode resonance in the antiferromagnetic phase.

Linear scaling of the Higgs mode width with its mass.

Abstract

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. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.