Universal Néel temperature in three-dimensional quantum antiferromagnets

Jin, Songbo; Sandvik, Anders W.

doi:10.1103/physrevb.85.020409

Cited by 21 publications

(57 citation statements)

References 24 publications

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“…Experimental and theoretical studies in this energy range can shed light on the Landau pole physics and on the expected dimensional crossover in TlCuCl 3 . Alternatively the Landau pole physics can be addressed in Quantum Monte Carlo studies of dimerized spin-lattice models [14,15].…”

Section: Figmentioning

confidence: 99%

Asymptotic freedom in quantum magnets

Scammell

Sushkov

2015

Phys. Rev. B

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Phase transitions in isotropic quantum antiferromagnets are described by an O(3) nonlinear quantum field theory. In three dimensions, the fundamental property of this theory is logarithmic scaling of the coupling constant. At the quantum critical point the coupling asymptotically vanishes and the quasiparticles become free. This logarithmic decay of the coupling constant has never been observed. In this paper, we derive finite temperature properties of the field theory and use our results to analyze the existing data on the real antiferromagnet TlCuCl3. Including finite temperatures into the theory, we find that agreement between theory and experiment is sufficiently sensitive to unambiguously identify the asymptotic decay of the coupling constant. We also comment on the unique possibility to study Landau pole-physics in quantum magnets.PACS numbers: 64.70. Tg, 75.40.Gb, 75.10.Jm Asymptotic freedom plays a crucial role in Quantum Chromodynamics. The freedom, which is due to nonabelian gauge fields, means a logarithmic decay of the coupling constant at high energies. Ultimately at infinite energies particles do not interact, this is ultraviolet asymptotic freedom [1,2]. In three dimensional (3D) non-gauge quantum field theories as well as in abelian gauge theories, the coupling constant decays logarithmically at low energies [3]. However, usually this decay is terminated because of a low energy cutoff. For example in Quantum Electrodynamics the cutoff is due to the rest energy of the electron. The low energy logarithmic decay can be observed only at a quantum critical point (QCP) where the cutoff energy is zero. It is known to the theory of quantum magnetism that certain antiferromagnetic systems can be driven to a QCP, and that at such a point the characteristic low energy magnetic excitations become non-interacting. At the QCP they experience "infrared asymptotic freedom". Quantum antiferromagnets in the vicinity of a QCP therefore provide a perfect testing ground for such behaviour. The low energy logarithmic decay of the coupling constant at a QCP can, in principle, be observed at zero temperature. The zero temperature case is well understood theoretically, a 3D quantum antiferromagnet at zero temperature is equivalent to a 4D classical antiferromagnet at finite temperature. The 3D QCP corresponds to the Néel transition in the 4D case. Thermodynamic quantities scale as powers of the running coupling constant [4]. Unfortunately, the existing zero temperature experimental data are not sufficient to pin down the logarithmic scaling. On the other hand combined zero and nonzero temperature data on TlCuCl 3 [5][6][7] provide an excellent opportunity to search for fingerprints of asymptotic freedom at the QCP. To perform this search we develop a theory of the QCP which accounts for both quantum and thermal fluctuations. After that we compare the theoretical predictions with experimental data. The comparison unambiguously indicates a logarithmically running cou- pling constant.The phase diagram of the dimerized 3D...

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Section: Figmentioning

confidence: 99%

Asymptotic freedom in quantum magnets

Scammell

Sushkov

2015

Phys. Rev. B

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“…The quantum Monte Carlo determination of T N and M s for the (3+1)-dimension ladder-dimer model is available in Ref. [16] as well. Notice that to quantitatively investigate the relation in Eq.…”

Section: Microscopic Model Andmentioning

confidence: 99%

Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

Kao

Jiang

2013

Eur. Phys. J. B

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We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation TN / √ c 3 ∝ Ms near the quantum critical point (QCP) associated with dimerization. Here TN , c, and Ms are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as TN and Ms, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation TN / √ c 3 ∝ Ms near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.Introduction.-While being the simplest models, Heisenberg-type models provide qualitatively, or even quantitatively useful information regarding the properties of cuprate materials. For example, the spatially anisotropic quantum Heisenberg model with different antiferromagnetic couplings in the 1 and 2 directions is demonstrated to be relevant for the underdoped cuprate superconductor YBa 2 Cu 3 O 6.45 [1,2]. Specifically, it is argued that this model provides a possible mechanism for the newly discovered pinning effects of the electronic liquid crystal in YBa 2 Cu 3 O 6.45 [3]. Because of their phenomenological importance, these models continue to attract a lot of attention analytically and numerically. In addition to being relevant to real materials, Heisenbergtype models on geometrically nonfrustrated lattices are important from a theoretical point of view as well. This is because these models can be simulated very efficiently using first principles Monte Carlo methods. Hence they are very useful in exploring ideas and examining theoretical predictions [4][5][6][7][8][9][10][11][12].

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“…Far more remarkably, an applied pressure also drives a QPT to an ordered phase [13], occurring at the very low critical pressure p c = 1.07 kbar [14] and sparking detailed studies [15,16]. This ordered phase is a different type of condensate, whose defining feature is a massive excitation, a "Higgs boson" or longitudinal fluctuation mode of the weakly ordered moment [17,18].…”

mentioning

confidence: 99%

Quantum and classical criticality in a dimerized quantum antiferromagnet

et al. 2014

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A quantum critical point (QCP) is a singularity in the phase diagram arising due to quantum mechanical fluctuations. The exotic properties of some of the most enigmatic physical systems, including unconventional metals and superconductors, quantum magnets, and ultracold atomic condensates, have been related to the importance of the critical quantum and thermal fluctuations near such a point. However, direct and continuous control of these fluctuations has been difficult to realize, and complete thermodynamic and spectroscopic information is required to disentangle the effects of quantum and classical physics around a QCP. Here we achieve this control in a high-pressure, high-resolution neutron scattering experiment on the quantum dimer material TlCuCl 3 . By measuring the magnetic excitation spectrum across the entire quantum critical phase diagram, we illustrate the similarities between quantum and thermal melting of magnetic order. We prove the critical nature of the unconventional longitudinal ("Higgs") mode of the ordered phase by damping it thermally. We demonstrate the development of two types of criticality, quantum and classical, and use their static and dynamic scaling properties to conclude that quantum and thermal fluctuations can behave largely independently near a QCP.In "classical" isotropic antiferromagnets, the excitations of the ordered phase are gapless spin waves emerging on the spontaneous breaking of a continuous symmetry [1]. The classical phase transition, occurring at the critical temperature T N , is driven by thermal fluctuations. In quantum antiferromagnets, quantum fluctuations suppress long-range order, and can destroy it completely even at zero temperature [2]. The ordered and disordered phases are separated by a quantum critical point (QCP), where quantum fluctuations restore the broken symmetry and all excitations become gapped, giving them characteristics fundamentally different from the Goldstone modes on the other side of the QCP (Fig. 1). At finite temperatures around a QCP, the combined effects of quantum and thermal fluctuations bring about a regime where the characteristic energy scale of spin excitations is the temperature itself, and this quantum critical (QC) regime has many special properties [3].Physical systems do not often allow the free tuning of a quantum fluctuation parameter through a QCP. The QC regime has been studied in some detail in heavy-fermion [14], and the green points depict the temperature and pressure values studied. Full details of this panel are presented in Fig. 4(c). The centre (E, T ) panel shows neutron intensity data collected from T = 1.8 K to 12.7 K at p = 1.75 kbar, where TN = 5.8 K. The rightmost (E, T ) panel shows the corresponding data at p = 3.6 kbar, where TN = 9.2 K. The data in both (E, T ) panels display a clear softening of the magnetic excitations at TN (p). The bottom (p, E) panel indicates the softening of the excitations, measured at T = 1.8 K, across the QPT [19]. T1, T2 and L denote the three gapped triplet excitations of th...

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Universal Néel temperature in three-dimensional quantum antiferromagnets

Cited by 21 publications

References 24 publications

Asymptotic freedom in quantum magnets

Asymptotic freedom in quantum magnets

Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

Quantum and classical criticality in a dimerized quantum antiferromagnet

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