Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.05563

Universal properties of three-dimensional random-exchange quantum antiferromagnets

D.-R. Tan, Fu-Jiun Jiang

Published Apr 21, 2015• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1504.05563

Related papers

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

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.

arXiv:1608.03835•Physical review. B./Physical review. B•Feb 28, 2017•8 citations

Universal scaling of three-dimensional dimerized quantum antiferromagnets on bipartite lattices

D.-R. Tan, Fu-Jiun Jiang

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 ${T}_{N}$ and the staggered magnetization density ${M}_{s}$ 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 ${T}_{N}$ and ${M}_{s}$ 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.

arXiv:1909.06971•Physical review. B./Physical review. B•Feb 14, 2020•3 citations

Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin- 12 antiferromagnets

D.-R. Tan, Fu-Jiun Jiang

The quantum critical regimes (QCR) of both a two-dimensional (2D) disordered spin-$\frac{1}{2}$ 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 ($T$) 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.

arXiv:1807.04456•Physical review. B./Physical review. B•Dec 10, 2018•3 citations

Universality in the three-dimensional random bond quantum Heisenberg antiferromagnet

Ulvi Kanbur, Erol Vatansever, Hamza Polat

The three-dimensional quenched random bond diluted $({J}_{1}\ensuremath{-}{J}_{2})$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ lattice up to $L=48$. By employing a standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio $r={J}_{2}/{J}_{1}$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional $O(3)$ Heisenberg universality class.

arXiv:2008.01464•Physical review. B./Physical review. B•Aug 14, 2020•6 citations

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

Munehisa Matsumoto, Chitoshi Yasuda, Synge Todo +1 more

The $S=1/2$ and $S=1$ two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for $S=1,$ we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.

arXiv:cond-mat/0107115•Physical review. B, Condensed matter•Nov 30, 2001•182 citations

Critical Temperature and the Transition from Quantum to Classical Order Parameter Fluctuations in the Three-Dimensional Heisenberg Antiferromagnet

Anders W. Sandvik

We present results of extensive quantum Monte Carlo simulations of the three-dimensional $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature ${T}_{\mathrm{c}}/J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.946\ifmmode\pm\else\textpm\fi{}0.001$. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous ${T}_{\mathrm{c}}>0$ phase transition.

arXiv:cond-mat/9804234•Physical Review Letters•Jun 8, 1998•108 citations
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.
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.
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.
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.
The three-dimensional quenched random bond diluted $({J}_{1}\ensuremath{-}{J}_{2})$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ lattice up to L=48L=48L=48. By employing a standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio r=J2/J1r={J}_{2}/{J}_{1}r=J2​/J1​. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional O(3)O(3)O(3) Heisenberg universality class.
The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
We present results of extensive quantum Monte Carlo simulations of the three-dimensional S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature ${T}_{\mathrm{c}}/J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.946\ifmmode\pm\else\textpm\fi{}0.001$. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc>0{T}_{\mathrm{c}}>0Tc​>0 phase transition.