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.
We investigate the quantum phase transition in an S=1/2 dimerized Heisenberg antiferromagnet in three spatial dimensions. By performing large-scale quantum Monte Carlo simulations and detailed finite-size scaling analyses, we obtain high-precision results for the quantum critical properties at the transition from the magnetically disordered dimer-singlet phase to the antiferromagnetically ordered N\'eel phase. This transition breaks O(N) symmetry with N=3 in D=3+1 dimensions. This is the upper critical dimension, where multiplicative logarithmic corrections to the leading mean-field critical properties are expected; we extract these corrections, establishing their precise forms for both the zero-temperature staggered magnetization ms and the N\'eel temperature TN. We present a scaling ansatz for TN, including logarithmic corrections, which agrees with our data and indicates exact linearity with ms, implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted N-independent leading and subleading logarithmic corrections in the size dependence of the staggered magnetic susceptibility. These logarithmic scaling forms have not previously been identified or verified by unbiased numerical methods, and we discuss their relevance to experimental studies of dimerized quantum antiferromagnets such as TlCuCl3.
We study the critical properties in cubic systems of antiferromagnetically coupled spin dimers near magnetic-field-induced quantum phase transitions. The quantum critical points in the zero-temperature phase diagram are determined from quantum Monte Carlo simulations. Furthermore, scaling properties of the uniform magnetization and the staggered transverse magnetization across the quantum phase transition in magnetic fields are calculated. Excellent agreement is observed between the quantum Monte Carlo simulations and previous analytical and experimental results near the magnetic field-induced transition. At the zero-field quantum critical point, logarithmic corrections to mean-field behavior are observed, which match well recent experiments for the pressure-induced quantum phase transition.
At the bulk upper critical dimension, marginally irrelevant interactions generate multiplicative logarithmic corrections to mean-field scaling. While these corrections are well understood for bulk observables, their consequences for boundary criticality, particularly for finite-size scaling, remain much less explored. Here we combine large-scale quantum Monte Carlo simulations with boundary renormalization-group analysis to study a (3 + 1)D O(3) quantum critical point. After verifying the known logarithmically modified bulk finite-size scaling, including the correlation-length scaling governed by the logarithmic finite-size exponent \hat{\coppa}, we tune the surface coupling to identify ordinary, special, and extraordinary boundary regimes. For the ordinary and special transitions, we derive logarithmic correction exponents and \hat{\coppa}-dependent finite-size scaling forms for boundary correlations, including results that have not been systematically established before. These predictions are quantitatively supported by Monte Carlo data. In the extraordinary regime, we find long-range surface magnetic order and a logarithmically enhanced surface-bulk correlation.
We resolve the nature of the quantum phase transition between antiferromagnetic and valence-bond solid ground states in square-lattice spin-1/2 magnets - the putative deconfined quantum-critical point. Using quantum Monte Carlo simulations of J-Q models, in which Heisenberg exchange J competes with multi-spin interactions Qn formed by n singlet projectors, we demonstrate first-order discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak and we extract universal scaling dimensions of a proximate multicritical point. Their values coincide closely with known bounds for an SO(5) symmetric conformal field theory (CFT) containing a relevant SO(5) singlet operator that destabilizes the generic deconfined critical point. We characterize the emergent SO(5) symmetry by its scaling dimensions of the leading irrelevant perturbations. Using the J-Q2-Q6 model, we tune the transition from weak to stronger first-order and find scaling of the coexisting order parameters with a large exponent beta ~ 0.85, in agreement with the relevant scaling dimensions of the multicritical point. The exponent that had previously been identified with the correlation length does not have a corresponding CFT level, and we explain it as pseudo-critical length scale of bubbles of one phase inside the other that are compressed in size by an SO(5)-violating irrelevant repulsive interaction between the two order parameters. The bubble scale reflects a hierarchy of excitation gaps generated by the SO(5) perturbation in the neighborhood of the first-order transition, akin to a Higgs mechanism. We argue that the multicritical point is the tip of a gapless spin liquid phase in frustrated Heisenberg models into which the J-Q models can be deformed, but the spin liquid, and perhaps the multicritical point itself, exist outside the regime amenable to sign-free simulations.
We study the XXZ square lattice bilayer model with antiferromagnetic non-frustrating long-range interactions that decay as a power law with the distance. Employing large-scale high-order series expansions with classical Monte Carlo integration (pCUT+MC) about the limit of isolated Heisenberg dimers in the rung-singlet phase, we investigate the one-triplon dispersion and the corresponding spectral weight along the parameter axes of the long-range decay exponent and the XXZ anisotropy. By tuning the latter, we observe two extended regions of 3d XY and Ising universality as well as 3d Heisenberg critical exponents at the isotropic point. Along the decay exponent axis, we demonstrate mean-field behavior for strong long-range couplings, the aforementioned three universality classes for sufficiently weak interactions, and continuously varying critical exponents in-between. Using extrapolations we are able to determine the one-triplon dispersion in a quantitative fashion up to the quantum-critical breakdown of the rung-singlet phase. This allows to extract the dynamical critical exponent z as a function of the decay exponent, displaying a universal behavior. The detected z<1 for small decay exponents is in agreement with the expected properties of the anomalous Goldstone modes in the ordered phases with broken continuous symmetry.
In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.