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arXiv:1506.06073 · Physical Review B

Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets

Yan Qin, Bruce Normand, Anders W. Sandvik, Zi Yang Meng

Published Dec 2, 2015• 29 citations
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Abstract

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 $\text{O}(N)$ 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 ${m}_{s}$ and the N\'eel temperature ${T}_{N}$. We present a scaling ansatz for ${T}_{N}$, including logarithmic corrections, which agrees with our data and indicates exact linearity with ${m}_{s}$, 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 ${\mathrm{TlCuCl}}_{3}$.

DOI
10.1103/physrevb.92.214401

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We investigate the quantum phase transition in an S=1/2S=1/2S=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)\text{O}(N)O(N) symmetry with N=3N=3N=3 in D=3+1D=3+1D=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{m}_{s}ms​ and the N'eel temperature TN{T}_{N}TN​. We present a scaling ansatz for TN{T}_{N}TN​, including logarithmic corrections, which agrees with our data and indicates exact linearity with ms{m}_{s}ms​, implying a complete decoupling of quantum and thermal fluctuation effects even arbitrarily close to the quantum critical point. We also demonstrate the predicted NNN-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{\mathrm{TlCuCl}}_{3}TlCuCl3​.
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.
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.
We study the Néel-paramagnetic quantum phase transition in two-dimensional dimerized S=1/2 Heisenberg antiferromagnets using finite-size scaling of quantum Monte Carlo data. We resolve the long-standing issue of the role of cubic interactions arising in the bond-operator representation when the dimer pattern lacks a certain symmetry. We find nonmonotonic (monotonic) size dependence in the staggered (columnar) dimerized model, where cubic interactions are (are not) present. We conclude that there is a new irrelevant field in the staggered model, but, at variance with previous claims, it is not the leading irrelevant field. The new exponent is ω_{2}≈1.25 and the prefactor of the correction L^{-ω_{2}} is large and comes with a different sign from that of the conventional correction with ω_{1}≈0.78. Our study highlights competing scaling corrections at quantum critical points.
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.
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 a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin-1/2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer (JcJ_cJc​) to intradimer (JDJ_DJD​) coupling is obtained as Jc/JD=0.3615(5)J_c/J_D = 0.3615(5)Jc​/JD​=0.3615(5). Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin-1/2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.