Pair supersolid of the extended Bose-Hubbard model with atom-pair hopping on the triangular Lattice

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of large-scale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.Comment: 6 pages, 7 figure

Rheological properties of polyurethane-based magnetorheological gels

© 2019 Zhang, Li, Wang and Wang. The paper tests the influence of mass fractions of carbonyl iron particles (CIPs) on the rheological properties of magnetorheological (MR) gels. Polyurethane-based MR gels with different weight fraction of CIPs, i.e., 40, 60, and 80%, were firstly prepared by mechanical mixing, respectively. The changes of shear stress and viscosity with shear rate under different magnetic flux density were tested and analyzed. It was found that the shear stress increases with mass fraction under magnetic flux density. The viscoelastic properties of MRGs were achieved by oscillatory shear measure. The effects of strain amplitude and frequency on viscoelastic of MRGs under different magnetic flux density were measured and analyzed. The study results shown that the elastic characteristics become more obvious with the increase of CIPs mass fraction. However, it has opposite effect on the viscous properties of materials

Anomalous quantum glass of bosons in a random potential in two dimensions

We present a quantum Monte Carlo study of the "quantum glass" phase of the 2D Bose-Hubbard model with random potentials at filling $\rho=1$. In the narrow region between the Mott and superfluid phases the compressibility has the form $\kappa \sim {\rm exp}(-b/T^\alpha)+c$ with $\alpha <1$ and $c$ vanishing or very small. Thus, at $T=0$ the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only $10\%$ changes the low-temperature compressibility by more than four orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp cross-over.Comment: Published version including supplementary material, 11 pages total, 15 figure

Low-Rank Graph Contrastive Learning for Node Classification

Graph Neural Networks (GNNs) have been widely used to learn node representations and with outstanding performance on various tasks such as node classification. However, noise, which inevitably exists in real-world graph data, would considerably degrade the performance of GNNs revealed by recent studies. In this work, we propose a novel and robust GNN encoder, Low-Rank Graph Contrastive Learning (LR-GCL). Our method performs transductive node classification in two steps. First, a low-rank GCL encoder named LR-GCL is trained by prototypical contrastive learning with low-rank regularization. Next, using the features produced by LR-GCL, a linear transductive classification algorithm is used to classify the unlabeled nodes in the graph. Our LR-GCL is inspired by the low frequency property of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. To the best of our knowledge, our theoretical result is among the first to theoretically demonstrate the advantage of low-rank learning in graph contrastive learning supported by strong empirical performance. Extensive experiments on public benchmarks demonstrate the superior performance of LR-GCL and the robustness of the learned node representations. The code of LR-GCL is available at \url{https://anonymous.4open.science/r/Low-Rank_Graph_Contrastive_Learning-64A6/}.Comment: arXiv admin note: text overlap with arXiv:2205.1410

Conducting-angle-based percolation in the XY model

We define a percolation problem on the basis of spin configurations of the two dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the existence of percolation transitions when the conducting angle is varied, and we determine the transition point for several values of the XY coupling. It appears that the critical behavior of this percolation model can be well described by the standard percolation theory. The critical exponents of the percolation transitions, as determined by finite-size scaling, agree with the universality class of the two-dimensional percolation model on a uniform substrate. This holds over the whole temperature range, even in the low-temperature phase where the XY substrate is critical in the sense that it displays algebraic decay of correlations.Comment: 16 pages, 14 figure

Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees

In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering original data with dimension $d$, we prove that, under some mild conditions, the perfect recovery of the cluster membership assignments of the convex clustering model, if exists, can be preserved by the randomly projected convex clustering model with embedding dimension $m = O(\epsilon^{-2}\log(n))$, where $0 < \epsilon < 1$ is some given parameter. We further prove that the embedding dimension can be improved to be $O(\epsilon^{-2}\log(K))$, which is independent of the number of data points. Extensive numerical experiment results will be presented in this paper to demonstrate the robustness and superior performance of the randomly projected convex clustering model. The numerical results presented in this paper also demonstrate that the randomly projected convex clustering model can outperform the randomly projected K-means model in practice