We prove that any symplectic matrix can be factored into no more than 5 unit triangular symplectic matrices, moreover, 5 is the optimal number. This result improves the existing triangular factorization of symplectic matrices which gives proof of 9 b
locks. We also show the corresponding improved conclusions for structured subsets of symplectic matrices.
A two-dimensional (2D) material with piezoelectricity, topological and ferromagnetic (FM) orders, namely 2D piezoelectric quantum anomalous hall insulator (PQAHI), may open new opportunities to realize novel physics and applications. Here, by first-p
rinciples calculations, a family of 2D Janus monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) with dynamic, mechanical and thermal stabilities is predict to be room-temperature PQAHI. At the absence of spin-orbit coupling (SOC), monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) is a half Dirac semimetal state. When the SOC is included, these monolayers become quantum anomalous hall (QAH) states with sizable gaps (more than two hundred meV) and two chiral edge modes (Chern number C=2). It is also found that monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) possesses robust QAH states against biaxial strain. By symmetry analysis, it is found that only out-of-plane piezoelectric response can be induced by a uniaxial strain in the basal plane. The calculated out-of-plane $d_{31}$ of $mathrm{Fe_2ICl}$ ($mathrm{Fe_2IBr}$) is 0.467 pm/V (0.384 pm/V), which is higher than or comparable with ones of other 2D known materials. Meanwhile, using Monte Carlo (MC) simulations, the Curie temperature $T_C$ is estimated to be 429/403 K for monolayer $mathrm{Fe_2ICl}$/$mathrm{Fe_2IBr}$ at FM ground state, which is above room temperature. Finally, the interplay of electronic correlations with nontrivial band topology is studied to confirm the robustness of QAH state. The combination of piezoelectricity, topological and FM orders makes monolayer $mathrm{Fe_2IX}$ (X=Cl and Br) become a potential platform for multi-functional spintronic applications with large gap and high $T_C$. Our works provide possibility to use the piezotronic effect to control QAH effects, and can stimulate further experimental works.
The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Ander
son insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.
It is highly desirable to search for promising two-dimensional (2D) monolayer materials for deep insight of 2D materials and applications. We use first-principles method to investigate tetragonal perovskite oxide monolayers as 2D materials. We find f
our stable 2D monolayer materials from SrTiO$_3$, LaAlO$_3$, KTaO$_3$, and BaFeO$_3$, denoting them as STO-ML, LAO-ML, KTO-ML, and BFO-ML. Our further study shows that through overcoming dangling bonds the first three monolayers are 2D wide-gap semiconducotors, and BFO-ML is a 2D isotropic Heisenberg ferromagnetic metal. There is a large electrostatic potential energy difference between the two sides, reflecting a large out-of-plane dipole, in each of the monolayers. These make a series of 2D monolayer materials, and should be useful in novel electronic devices considering emerging phenomena in perovskite oxide heterostructures.
For spintronics applications, it is highly desirable to realize highly-spin-polarized two-dimensional (2D) electron systems in electrically-controllable epitaxial ultrathin films on semiconductor substrates. Through systematic first-principles invest
igation, we propose the TcO$_2$ uni-cell layer (one-unit-cell thickness) on rutile TiO$_2$ (001) substrate as a semiconductor heterostructure and use electric field to manipulate its electronic and magnetic properties. Our study shows that the heterostructure is a narrow-gap semiconductor with an antiferromagnet-like ordering when the applied electric field is less than 0.026 V/AA{}, and then it transits to a half-metallic ferrimagnet with 100% spin polarization. Our further analysis indicates that the magnetization density and the electronic states near the Fermi level originate mainly from the TcO$_2$ uni-cell layer, with the remaining minor part from the interfacial Ti-O$_2$ monolayers, and the bonds and bond angles quickly converge to the corresponding values of bulk TiO$_2$ when crossing the interface and entering the TiO$_2$ layer. Therefore, the heterostructure is actually a 2D electron system determined by the TcO$_2$ uni-cell layer and the TiO$_2$ substrate. Because the half-metallic phase with 100% spin polarization can be achieved at 0.026 V/AA{}, this epitaxial 2D electron system should be usable in spintronics applications.
Recent studies of pairing and charge order in materials such as FeSe, SrTiO$_3$, and 2H-NbSe$_2$ have suggested that momentum dependence of the electron-phonon coupling plays an important role in their properties. Initial attempts to study Hamiltonia
ns which either do not include or else truncate the range of Coulomb repulsion have noted that the resulting spatial non-locality of the electron-phonon interaction leads to a dominant tendency to phase separation. Here we present Quantum Monte Carlo results for such models in which we incorporate both on-site and intersite electron-electron interactions. We show that these can stabilize phases in which the density is homogeneous and determine the associated phase boundaries. As a consequence, the physics of momentum dependent electron-phonon coupling can be determined outside of the trivial phase separated regime.
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the syst
em towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $xi$, interpolating between the Holstein and Frohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $xi$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U e 0$ case, even for small values of the coupling range.
We propose using a directional time-varying (rotating) driving magnetic field to suppress magneto-Rayleigh-Taylor (MRT) instability in dynamic Z-pinches. A rotational drive magnetic field is equivalent to two magnetic-field components, {Theta} and Z,
that alternate in time, referred to as an alternate Theta-Z-pinch configuration. We consider the finitely thick cylindrical liner configuration in this paper. We numerically integrate the perturbation equation to stagnation time based on the optimal background unperturbed trajectories. We assess the cumulative growth of the dominant mode selected by some mechanism at the beginning of an implosion. The maximum e-folding number at stagnation of the dominant mode of an optimized alternate Theta-Z-pinch is significantly lower than that of the standard Theta- or Z-pinch. The directional rotation of the magnetic field contributes to suppress the instabilities, independent of the finite thickness. The finite thickness effect plays a role only when the orientation of the magnetic field varies in time whereas it does not appear in the standard Theta- or Z-pinch. The rotating frequency of the magnetic field and the thickness of liner are both having a monotonic effect on suppression. Their synergistic effect can enhance the suppression on MRT instability. Because the MRT instability can be well suppressed in this way, the alternate Theta-Z-pinch configuration has potential applications in liner inertial fusion. This work is supported by the NSFC (Grant Nos. 11405167, 51407171, 11571293, 11605188, and 11605189) and the Foundation of the China Academy of Engineering Physics (No. 2015B0201023).
In this work, we make two improvements on the staggered grid hydrodynamics (SGH) Lagrangian scheme for modeling 2-dimensional compressible multi-material flows on triangular mesh. The first improvement is the construction of a dynamic local remeshing
scheme for preventing mesh distortion. The remeshing scheme is similar to many published algorithms except that it introduces some special operations for treating grids around multi-material interfaces. This makes the simulation of extremely deforming and topology-variable multi-material processes possible, such as the complete process of a heavy fluid dipping into a light fluid. The second improvement is the construction of an Euler-like flow on each edge of the mesh to count for the edge-bending effect, so as to mitigate the checkerboard oscillation that commonly exists in Lagrangian simulations, especially the triangular mesh based simulations. Several typical hydrodynamic problems are simulated by the improved staggered grid Lagrangian hydrodynamic method to test its performance.
We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N log^2 N $ work), we can solve linear systems with this matrix with $N log N $ work. Kern
el matrices represent pairwise interactions of points in metric spaces. They appear in machine learning, approximation theory, and computational physics. Kernel matrices are typically dense (matrix multiplication scales quadratically with $N$) and ill-conditioned (solves can require 100s of Krylov iterations). Thus, fast algorithms for matrix multiplication and factorization are critical for scalability. Recently we introduced ASKIT, a new method for approximating a kernel matrix that resembles N-body methods. Here we introduce INV-ASKIT, a factorization scheme based on ASKIT. We describe the new method, derive complexity estimates, and conduct an empirical study of its accuracy and scalability. We report results on real-world datasets including COVTYPE ($0.5$M points in 54 dimensions), SUSY ($4.5$M points in 8 dimensions) and MNIST (2M points in 784 dimensions) using shared and distributed memory parallelism. In our largest run we approximately factorize a dense matrix of size 32M $times$ 32M (generated from points in 64 dimensions) on 4,096 Sandy-Bridge cores. To our knowledge these results improve the state of the art by several orders of magnitude.
