Excitation Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

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.

4 pages, 4 figures 2 pages, 2 figures supplemental material

References in corpus (12)

• Quantum magnetism and criticality
• Amplitude / Higgs Modes in Condensed Matter Physics
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Quantum and classical criticality in a dimerized quantum antiferromagnet
• The Higgs mode in a two-dimensional superfluid
• The amplitude mode in three-dimensional dimerized antiferromagnets
• A new critical exponent koppa and its logarithmic counterpart koppa-hat
• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets I: Paramagnetic phase
• Spectral function of the Higgs mode in 4-\varepsilon dimensions
• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets II: Antiferromagnetic phase and quantum phase transition
• Linked-cluster expansions for quantum magnets on the hypercubic lattice

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• Nutation Wave as a Platform for Ultrafast Spin Dynamics in Ferromagnets
• Diagnosing Fractionalization from the Spin Dynamics of $Z_2$ Spin Liquids on the Kagome Lattice by Quantum Monte Carlo Simulations
• Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions
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• Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models
• Phase transitions in the spin-1/2 Heisenberg antiferromagnet on the dimerized diamond lattice
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions