We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four-and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N ), we also find continuous transitions for N = 3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.PACS numbers: 75.10. Jm, 75.10.Nr, 75.40.Mg, 75.40.Cx Two-dimensional quantum spin system with nonmagnetic ground states have been at the forefront of condensed matter physics for more than two decades [1,2,3,4]. Frustrated system have been investigated intensly [5], but large-scale unbiased computational studies of their ground states are not possible, due to the "sign problems" hampering quantum Monte Carlo (QMC) methods [6]. It was recently realized that one prominent class of non-magnetic states-valence-bond solids (VBSs)-can be accessed also without frustration, by adding certain multi-spin interactions to the standard S = 1/2 Heisenberg antiferromagnet [7]. These models enable detailed QMC studies of the antiferromagnetic (AF) to VBS quantum phase transition. It has been argued that this transition is associated with spinon deconfinement (hence the term deconfined quantum criticality) and should, due to subtle quantum interference effects, be continuous [3]. This scenario violates the "Landau rule", according to which a direct transition between states breaking unrelated symmetries should be generically first-order.The theory of deconfined quantum criticality has generated a great deal of interest, as well as controversy [7,8,9,10,11,12,13,14,15]. Numerical studies of a Heisenberg hamiltonian with 4-spin interactions are generally in good agreement with the theory, showing a continuous transition with dynamic exponent z = 1, large spin correlation exponent η s , and an emergent U(1) symmetry [7,8,9]. Arguments for a first-order transition have also been put forward [11,14], based on numerical studies of lattice versions of the field-theory proposed [3] to capture the AF-VBS transition. Other, similar studies reach different conclusions, however [13]. Further studies are thus called for.In this Letter, we advance computational studies of the AF-VBS transition in two different ways. First, we consider the S = 1/2 Heisenberg model including 4-spin and 6-spin interactions. The unperturbed Heisenberg model is defined by the hamiltonianwhere ij denotes nearest neighbors on a periodic square lattice with L 2 sites andis the two-spin singlet projector. In the "J-Q" model introduced in [7], the following term is added to H 1 ;The spin pairs ij and kl are located on adjacent corners of a 4-site plaquette, as illustrated in Fig. 1. We denote the strength of the 4-spin term Q 2 , with the subscript indicating two singlet projectors, and also consid...
Competition between electronic ground states near a quantum critical point (QCP)--the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations--is expected to lead to unconventional behaviour in low-dimensional systems. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture. Here we show evidence that the Bose-Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12-16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-(1/2) Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an 'emergent' nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.
Besides being an ancient pigment, BaCuSi2O6 is a quasi-2D magnetic insulator with a gapped spin dimer ground state. The application of strong magnetic fields closes this gap, creating a gas of bosonic spin triplet excitations. The topology of the spin lattice makes BaCuSi2O6 an ideal candidate for studying the Bose-Einstein condensation of triplet excitations as a function of the external magnetic field, which acts as a chemical potential. In agreement with quantum Monte Carlo numerical simulations, we observe a distinct lambda anomaly in the specific heat together with a maximum in the magnetic susceptibility upon cooling down to liquid helium temperatures.
We have studied the three-dimensional Ising spin glass with a J distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a nite size scaling analysis shows quite strong evidence for a nite transition temperature, Tc, with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, , is somewhat higher. Because there may be (unknown) corrections to nite size scaling, we do not completely rule out the possibility that Tc = 0 or that Tc is nite but with no order below Tc. However, from our data, these possibilities seem less likely.The question of whether there is a nite transition temperature, T c , in an Ising spin glass in three dimensions has aroused a lot of interest for the last two decades 1 , and the consensus of opinion has changed several times. About one decade ago, several pieces of work 2{5 seemed to show that there is a nite T c , and this conclusion has generally been restated since then 6 . However, on closer inspection, the case is not completely closed. For example, the work of one of us 2 , henceforth referred to as BY, is unable to rule out the possibility that T c = 0 and the correlation length, , diverges exponentially as T ! 0, as happens in the two-dimensional Heisenberg ferromagnet.
NiCl2-4SC(NH2)2 (DTN) is a quantum S = 1 chain system with strong easy-pane anisotropy and a new candidate for the Bose-Einstein condensation of the spin degrees of freedom. ESR studies of magnetic excitations in DTN in fields up to 25 T are presented. Based on analysis of the single-magnon excitation mode in the high-field spin-polarized phase and previous experimental results [ Phys. Rev. Lett. 96, 077204 (2006)], a revised set of spin-Hamiltonian parameters is obtained. Our results yield D = 8.9 K, Jc = 2.2 K, and J a,b = 0.18 K for the anisotropy, intrachain, and interchain exchange interactions, respectively. These values are used to calculate the antiferromagnetic phase boundary, magnetization and the frequency-field dependence of two-magnon bound-state excitations predicted by theory and observed in DTN for the first time. Excellent quantitative agreement with experimental data is obtained. PACS numbers: 75.40.Gb, 75.10.Jm Antiferromagnetic (AFM) quantum spin-1 chains have been the subject of intensive theoretical and experimental studies, fostered especially by the Haldane conjecture [1]. Due to quantum fluctuations, an isotropic spin-1 chain has a spin-singlet ground state separated from the first excited state by a gap ∆ ∼ 0.41J [2], where J is the exchange interaction. As shown by Golinelli et al. [3], the presence of a strong easy-plane anisotropy D can significantly modify the excitation spectrum, so that the gap size is not determined by the strength of the AFM quantum fluctuations exclusively, but depends on the dimensionless parameter ρ = D/J. The Haldane phase is predicted to survive up to ρ c = 0.93 [4], where the system undergoes a quantum phase transition. For ρ > ρ c the gap reopens, but its origin is dominated by the anisotropy D, and the system is in the so-called large-D regime. While the underlying physics of Haldane chains is fairly well understood, relatively little is known about the magnetic properties (and particularly the elementary excitation spectrum) of nonHaldane S = 1 AFM chains in the large-D phase. Intense theoretical work and numerous predictions [3,4,5,6,7,8,9,10] make the experimental investigation of large-D spin-1 chains a topical problem in low-dimensional magnetism.Recently, weakly-coupled spin-1 chains have attracted renewed interest due to their possible relevance to the fieldinduced Bose-Einstein condensation (BEC) of magnons. When the field H, applied perpendicular to the easy plane, exceeds a critical value H c1 (defined at T = 0), the gap closes and the system undergoes a transition into an XY -like AFM phase with a finite magnetization and AFM magnon excitations. If the spin Hamiltonian has axial symmetry with respect to the applied field, the AFM ordering can be described as BEC of magnons by mapping the spin-1 system into a gas of semi-hard-core bosons [11]. The applied field plays the role of a chemical potential, changing the boson population. In accordance with mean-field BEC theory [12,13,14], the phasediagram boundary for a three-dimensional system sh...
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