The N\'eel temperature, staggered magnetization density, as well as the spin-wave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first-principles nonperturbative quantum Monte Carlo simulations. In particular, we examine the validity of universal scaling relations that are related to these three studied physical quantities. These relations are relevant to experimental data and are firmly established for clean (regular) 3D dimerized spin-1/2 Heisenberg models. Remarkably, our numerical results show that the considered scaling relations remain true for the investigated model with the introduced disorder. In addition, while the presence of disorder may change the physical properties of regular dimerized models, hence leading to different critical theories, both the obtained data of N\'eel temperature and staggered magnetization density in our study are fully compatible with the expected critical behavior for clean dimerized systems. As a result, it is persuasive to conclude that the related quantum phase transitions of the considered disordered model and its clean analogues are governed by the same critical theory, which is not always the case in general. Finally, we also find smooth scaling curves even emerging when both the data of the investigated disordered model as well as its associated clean system are taken into account concurrently. This in turn implies that, while in a restricted sense, the considered scaling relations for 3D spin-1/2 antiferromagnets are indeed universal.
The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.
The thermal and ground state properties of a class of three-dimensional (3D) random-exchange spin-1/2 antiferromagnets are studied using first principles quantum Monte Carlo method. Our motivation is to examine whether the newly discovered universal properties, which connect the Néel temperature and the staggered magnetization density, for the clean 3D quantum dimerized Heisenberg models remain valid for the random-exchange models considered here. Remarkably, similar to the clean systems, our Monte Carlo results indicate that these universal relations also emerge for the considered models with the introduced antiferromagnetic randomness. The scope of the validity of these universal properties for the 3D quantum antiferromagnets is investigated as well.
A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a specific kind of quenched disorder is investigated, using the first-principles nonperturbative quantum Monte Carlo calculations (QMCs). The employed disorder distribution has a tunable parameter
p which can be considered as a measure of randomness (
p=0 correponds to the clean model). Through large-scale QMCs, the dynamic critical exponents
z, the ground-state energy densities
E0, and the Wilson ratios
W of various
p are determined with high precision. Interestingly, we find that the
p dependencies of
z and
W are likely to be complementary to each other. For instance, while the
z values of $0.4\ensuremath{\le}p\ensuremath{\le}0.9$ match well among themselves and are statistically different from that of
p=0, the
W values for
p<0.7 are in reasonably good agreement with $W\ensuremath{\sim}0.1243$ of the clean case. Surprisingly, our study indicates that a threshold of randomness,
pW, associated with
W exists. In particular, beyond this threshold the magnitude of
W grows with
p. This is somehow counterintuitive since one expects the spin correlations should diminish accordingly. Similarly, there is a threshold
pz related to
z after which a constant value is obtained for
z. The results presented here are not only interesting from a theoretical perspective but also can serve as benchmarks for future related studies.
Abstract By simulating a two-dimensional dimerized spin-1/2 antiferromagnet with the quantum Monte Carlo method, the numerical values of two universal quantities associated with the quantum critical regime (QCR), namely
S(π,π)/(χsT) S ( π , π ) / χ s T and
c/(Tξ) c / T ξ , are determined. Here
S(π,π) S ( π , π ) ,
χs χ s , c ,
ξ, ξ , and T are the staggered structure factor, the staggered susceptibility, the spin-wave velocity, the correlation length, and the temperature, respectively. Our calculations lead to
S(π,π)/(χsT)∼1.073 S ( π , π ) / χ s T ∼ 1.073 and
c/(Tξ)∼0.963 c / T ξ ∼ 0.963 , which are in better consistency with the leading theoretical predictions than those including the next-to-leading-order terms. This scenario was also observed for the Wilson ratio W and
χuc2/T χ u c 2 / T (
χu χ u is the uniform susceptibility) of QCR. The presented outcomes here and those in the literature suggest that it is desirable to conduct a refined analytic calculation to resolve the puzzle of why the inclusion of higher-order terms leads to less accurate predictions for these universal quantities. Graphical abstract
S(π,π)/(χsT) S ( π , π ) /
Using the first-principles quantum Monte Carlo calculations, we investigate the previously established universal scaling, as well as the corresponding classification schemes, for the N\'eel temperature
TN and the staggered magnetization density
Ms of three-dimensional dimerized quantum antiferromagnets. Particularly, the calculations are done on both the stacked honeycomb and cubic lattices. In addition to simulating models with two types of antiferromagnetic couplings (bonds) like those examined in earlier studies, here a tunable parameter controlling the strength of the third type of bond is introduced. Interestingly, while minor effects due to microscopic details appear, the data for the studied models with two types of bonds do fall on top of the universal scaling curves determined previously. Moreover, the most striking result suggested in our study is that with the presence of three kinds of bonds in the investigated models, the considered scaling relations between
TN and
Ms can be classified by the coordination number of the underlying lattice geometries. The findings presented here broaden the applicability of the associated classification schemes formerly discovered. In particular, these results not only are interesting from a theoretical point of view but also can serve as useful guidelines for the relevant experiments.