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...

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(N ) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(N ) Néel and valence-bond solid phases is characterized for N = 2, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (L = 256) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent y ≡ 1/ν as the system size increases. We also confirm the relevance of a squared valence-bond solid field 2 for the SU(3) model.

This study investigates the motivational factors affecting the quantity and quality of voluntary knowledge contribution in online Q&A communities. Although previous studies focus on knowledge contribution quantity, this study regards quantity and quality as two important, yet distinct, aspects of knowledge contribution. Drawing on self-determination theory, this study proposes that five motivational factors, categorized along the extrinsicintrinsic spectrum of motivation, have differential effects on knowledge contribution quantity versus quality in the context of online Q&A communities. An online survey with 367 participants was conducted in a leading online Q&A community to test the research model. Results show that rewards in the reputation system, learning, knowledge self-efficacy, and enjoy helping stand out as important motivations. Furthermore, rewards in the reputation system, as a manifestation of the external regulation, is more effective in facilitating the knowledge contribution quantity than quality. Knowledge selfefficacy, as a manifestation of intrinsic motivation, is more strongly related to knowledge contribution quality, whereas the other intrinsic motivation, enjoy helping, is more strongly associated with knowledge contribution quantity. Both theoretical and practical implications are discussed.

We study the three-dimensional XY model with a Zq anisotropic term. At temperatures T

We study a variational wave function for the ground state of the two-dimensional S =1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h͑x , y͒ for valence bonds connecting spins separated by ͑x , y͒ lattice spacings. In contrast to previous studies, in which a functional form for h͑x , y͒ was assumed, we here optimize all the amplitudes for lattices with up to 32ϫ 32 spins. We use two different schemes for optimizing the amplitudes; a Newton conjugate-gradient method and a stochastic method which requires only the signs of the first derivatives of the energy. The latter method performs significantly better. The energy for large systems deviates by only Ϸ0.06% from its exact value ͑calculated using unbiased quantum Monte Carlo simulations͒. The spin correlations are also well reproduced, falling Ϸ2% below the exact ones at long distances ͑corresponding to an Ϸ1% underestimation of the sublattice magnetization͒. The amplitudes h͑r͒ for valence bonds of long length r decay as r −3 . We also discuss some results for small frustrated lattices.