Shift insulators: rotation-protected two-dimensional topological crystalline insulators

We study a two-dimensional (2D) tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g. $p_\pm$ orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. In addition, we show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed upon the addition of appropriate atomic orbitals, which implies `fragile' topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients. Following the analysis of the model, which serves as a prototypical example of 2D TCIs protected by rotation, we show that all TCIs protected by point group symmetries which do not have protected surface states are either atomic insulators or fragile phases. Remarkably, this implies that gapless surface states exist in free electron systems if and only if there is a stable Wannier obstruction. We then use dimensional reduction to map the problem of classifying 2D TCIs protected by rotation to a zero-dimensional (0D) problem which is then used to obtain the complete non-interacting classification of such TCIs as well as the reduction of this classification in the presence of interactions.Comment: 33 pages, 16 figure

Accelerated Variance Reduced Stochastic ADMM

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T) as opposed to O(1/T^2) of accelerated batch algorithms, where $T$ is the number of iterations. Thus, there still remains a gap in convergence rates between existing stochastic ADMM and batch algorithms. To bridge this gap, we introduce the momentum acceleration trick for batch optimization into the stochastic variance reduced gradient based ADMM (SVRG-ADMM), which leads to an accelerated (ASVRG-ADMM) method. Then we design two different momentum term update rules for strongly convex and general convex cases. We prove that ASVRG-ADMM converges linearly for strongly convex problems. Besides having a low per-iteration complexity as existing stochastic ADMM methods, ASVRG-ADMM improves the convergence rate on general convex problems from O(1/T) to O(1/T^2). Our experimental results show the effectiveness of ASVRG-ADMM.Comment: 16 pages, 5 figures, Appears in Proceedings of the 31th AAAI Conference on Artificial Intelligence (AAAI), San Francisco, California, USA, pp. 2287--2293, 201

Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization

The Schatten-p quasi-norm $(0<p<1)$ is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we first define two tractable Schatten quasi-norms, i.e., the Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively, which lead to the design of very efficient algorithms that only need to update two much smaller factor matrices. We also design two efficient proximal alternating linearized minimization algorithms for solving representative matrix completion problems. Finally, we provide the global convergence and performance guarantees for our algorithms, which have better convergence properties than existing algorithms. Experimental results on synthetic and real-world data show that our algorithms are more accurate than the state-of-the-art methods, and are orders of magnitude faster.Comment: 16 pages, 5 figures, Appears in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), Phoenix, Arizona, USA, pp. 2016--2022, 201

RW Aur A from the X-Wind Point of View: General Features

In this paper, the RW Aur A microjet is studied from the point of view of X-wind models. The archived HST/STIS spectra of optical forbidden lines [O I], [S II], and [N II] from RW Aur A, taken in Cycle 8 with seven parallel slits along the jet axis, spaced at 0".07 apart, were analyzed. Images, position-velocity diagrams, and line ratios among the species were constructed, and compared with synthetic observations generated by selected solutions of the X-wind. Prominent features arising in a steady state X-wind could be identified within the convolved images, full-widths at half maxima and high-velocity peaks on both of the redshifted and blueshifted jets. The well-known asymmetric velocity profiles of the opposite jets are built into the selected models. We discuss model selections within the existing uncertainties of stellar parameters and inclination angle of the system. In this framework, the mass-loss rates that were inferred to be decreasing along the jet axis in the literature are the results of slowly decreasing excitation conditions and electron density profiles. Despite the apparent asymmetry in terminal velocities, line intensities and mass-loss rates, the average linear momenta from the opposite sides of the jet are actually balanced. These previously hard-to-explain features of the asymmetric RW Aur A jet system now find a different but self-consistent interpretation within the X-wind framework.Comment: 31 pages, 9 figures, 5 tables; accepted for publication in ApJ (Send correspondence to: [email protected]

Tracking ocean heat uptake during the surface warming hiatus.

Ocean heat uptake is observed to penetrate deep into the Atlantic and Southern Oceans during the recent hiatus of global warming. Here we show that the deep heat penetration in these two basins is not unique to the hiatus but is characteristic of anthropogenic warming and merely reflects the depth of the mean meridional overturning circulation in the basin. We find, however, that heat redistribution in the upper 350 m between the Pacific and Indian Oceans is closely tied to the surface warming hiatus. The Indian Ocean shows an anomalous warming below 50 m during hiatus events due to an enhanced heat transport by the Indonesian throughflow in response to the intensified trade winds in the equatorial Pacific. Thus, the Pacific and Indian Oceans are the key regions to track ocean heat uptake during the surface warming hiatus