Width of the longitudinal magnon in the vicinity of the O(3) quantum critical point

Kulik, Yakov; Sushkov, O. P.

doi:10.1103/physrevb.84.134418

Cited by 39 publications

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“…3). Both findings establish the amplitude mode as a relatively broad, critically well-defined excitation on the bicube lattice, as observed also in experiments [17,18] on TlCuCl 3 and within field-theory calculations [4,21]. In summary, we provided robust evidence for the presence of multiplicative logarithmic corrections to the leading Gaussian mean-field scaling of the triplon excitation gap softening near the quantum critical point.…”

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confidence: 59%

“…In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.Quantum critical three-dimensional antiferromagnets provide considerably valuable condensed matter realizations of (infrared) asymptotically free quantum field theories: based on the quantum-to-classical mapping, the critical field theory that describes the underlying quantum critical point is the classical four-dimensional O(3) φ 4 -theory [1][2][3][4][5][6]. Due to a logarithmic decay of the renormalized interaction strength upon approaching the critical point, this field theory exhibits logarithmic corrections to a Gaussian fixed point [7][8][9][10].…”

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Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

Lohöfer

Wessel

2017

Phys. Rev. Lett.

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By means of large-scale quantum Monte Carlo simulations, we examine the quantum critical scaling of the magnetic excitation gap (the triplon gap) in a three-dimensional dimerized quantum antiferromagnet, the bicubic lattice, and identify characteristic multiplicative logarithmic scaling corrections atop the leading mean-field behavior. These findings are in accord with field-theoretical predictions that are based on an effective description of the quantum critical system in terms of an asymptotically-free field theory, which exhibits a logarithmic decay of the renormalized interaction strength upon approaching the quantum critical point. Furthermore, using bond-based singlet spectroscopy, we identify the amplitude (Higgs) mode resonance within the antiferromagnetic region. We find a Higgs mass scaling in accord with field-theoretical predictions that relate it by a factor of √ 2 to the corresponding triplon gap in the quantum disordered regime. In contrast to the situation in lower-dimensional systems, we observe in this three-dimensional coupled-dimer system a distinct signal from the amplitude mode also in the dynamical spin structure factor. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.Quantum critical three-dimensional antiferromagnets provide considerably valuable condensed matter realizations of (infrared) asymptotically free quantum field theories: based on the quantum-to-classical mapping, the critical field theory that describes the underlying quantum critical point is the classical four-dimensional O(3) φ 4 -theory [1][2][3][4][5][6]. Due to a logarithmic decay of the renormalized interaction strength upon approaching the critical point, this field theory exhibits logarithmic corrections to a Gaussian fixed point [7][8][9][10]. This leads to characteristic multiplicative logarithmic scaling corrections to the bare mean-field behavior in various physical quantities that are in principle accessible by several experimental probes, such as in thermodynamic measurements or neutron and light scattering techniques [6,[11][12][13][14], if probed at the relevant energy scales near the quantum critical point.A well characterized example system of this scenario is provided by the dimerized spin-half compound TlCuCl 3 : under the application of hydrostatic pressure, this system features a quantum phase transition from a gapped quantum disordered state into an antiferromagnetically ordered phase [15]. The magnetic excitations across the quantum critical region have been analyzed in detail recently by inelastic neutron scattering [16][17][18]. These studies identified the evolution of the gapped magnon mode from the dimerized quantum disordered regime (frequently referred to also as the "triplon" mode in reference to its threefold degeneracy in the isotropic Heisenberg spin-exchange case), to the low-energy (transverse) Goldstone modes that accompany the spontaneous bre...

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confidence: 59%

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confidence: 99%

Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

Lohöfer

Wessel

2017

Phys. Rev. Lett.

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“…In this case the mass squared term in the magnon Lagrangian changes sign at the transition [20]. Now we consider a similar QPT for spinons described by the Lagrangian (1), m 2 ∝ g − g c .…”

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Violation of the Spin-Statistics Theorem and the Bose-Einstein Condensation of Particles with Half-Integer Spin

Scammell

Sushkov

2015

Phys. Rev. Lett.

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We consider the Bose condensation of particles with spin 1/2. The condensation is driven by an external magnetic field. Our work is motivated by ideas of quantum critical deconfinement and bosonic spinons in spin liquid states. We show that both the nature of the novel Bose condensate and the excitation spectrum are fundamentally different from that in the usual integer spin case. We predict two massive ("Higgs") excitations and two massless Goldstone excitations. One of the Goldstone excitations has a linear excitation spectrum and another has quadratic spectrum. This implies that the Bose condensate does not support superfluidity, the Landau criterion is essentially violated. We formulate a "smoking gun" criterion for searches of the novel Bose condensation.PACS numbers: 64.70. Tg, 75.40.Gb, 75.10.Jm The phenomenon of Bose-Einstein condensation [1,2] is of enormous importance in physics, from superfluidity of liquid 4 He [3-5] to cold atoms [6]. The famous spinstatistics theorem [7] claims that particles with integer spin obey Bose statistics and particles with half integer spin obey Fermi statistics. Therefore only particles with integer spin can Bose condensate [8]. The spin statistic relation is based on Lorentz invariance, so the relation is a relativistic effect which is absolutely important even at extremely low energy. If the number of particles is conserved the stability of Bose condensate is not related to interaction between bosons. The repulsive interaction is only responsible for a linear in momentum spectrum of Goldstone excitations [5]. The linear spectrum guarantees superfluidity of the Bose condensate [4]. If the number of particles is not conserved, like in the case of magnetic field induced Bose condensation of magnons in a gapped quantum antiferromagnet [9,10], then the stability of the condensate is only due to repulsion between particles. The excitation spectrum above the condensate is still linear in momentum. The linearity is a generic property of a conventional Bose condensation.The idea of bosonic quasiparticles with spin 1/2, spinons, is a new paradigm in condensed matter physics. Bosonic spinons have been proposed as quasiparticles in some kinds of spin liquids [11]. Bosonic spinons also appear in the deconfined quantum criticality (DQC) scenario. The scenario has been suggested [12, 13] to explain properties of a magnetic quantum phase transition between a Neel antiferromagnet (AF) and a valence-bond solid (VBS) in a two-dimensional system of S=1/2 spins. According to this scenario the system fractionalize into independent (deconfined) spinons. Bosonic spinons do not contradict the spin statistics theorem since they are quasiparticles in a solid and hence the Lorentz invariance is explicitly violated. Both the spin liquid and the DQC are essentially strong coupling nonperturbative phenomena, therefore there is no simple theoretical model where the phenomena can be studied analytically. There are several spin-lattice models which, according to numerical studies, manifest the spin ...

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“…Recently a new universal behavior between the thermal and quantum properties of (3+1)-dimensional dimerized quantum antiferromagnets has been established [14,15]. Specifically, using the relevant field theory, it is shown that the Néel temperature T N can be related to the staggered magnetization density M s near a quantum critical point (QCP).…”

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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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Width of the longitudinal magnon in the vicinity of the O(3) quantum critical point

Cited by 39 publications

References 28 publications

Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

Violation of the Spin-Statistics Theorem and the Bose-Einstein Condensation of Particles with Half-Integer Spin

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

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