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arXiv:1608.03835 · Physical review. B./Physical review. B

Universal scaling of Néel temperature, staggered magnetization density, and spin-wave velocity of three-dimensional disordered and clean quantum antiferromagnets

D.-R. Tan, Fu-Jiun Jiang

Published Feb 28, 2017• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.054435

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The quantum critical regimes (QCR) of both a two-dimensional (2D) disordered spin-12\frac{1}{2}21​ antiferromagnet and a 2D clean dimerized quantum Heisenberg model are studied using the first-principles nonperturbative quantum Monte Carlo simulations. In particular, the three well-known universal coefficients associated with QCR are investigated in detail. While in our investigation we find the obtained results are consistent with the related analytic predictions, non-negligible finite-temperature (TTT) effects are observed. Moreover, a striking finding in our study is that the numerical value for one of the universal coefficients we determine is likely to be different significantly from the corresponding (theoretical) result(s) established in the literature. To better understand the sources for the discrepancy observed here, apart from carrying out the associated analytic calculations not considered previously, it will be desirable as well to conduct a comprehensive examination of the exotic features of QCR for other disordered and clean spin systems than those investigated in this study.
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{T}_{N}TN​ and the staggered magnetization density Ms{M}_{s}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{T}_{N}TN​ and Ms{M}_{s}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.
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