865 research outputs found
Localization and Mobility Gap in Topological Anderson Insulator
It has been proposed that disorder may lead to a new type of topological
insulator, called topological Anderson insulator (TAI). Here we examine the
physical origin of this phenomenon. We calculate the topological invariants and
density of states of disordered model in a super-cell of 2-dimensional
HgTe/CdTe quantum well. The topologically non-trivial phase is triggered by a
band touching as the disorder strength increases. The TAI is protected by a
mobility gap, in contrast to the band gap in conventional quantum spin Hall
systems. The mobility gap in the TAI consists of a cluster of non-trivial
subgaps separated by almost flat and localized bands.Comment: 8 pages, 7 figure
A Minimal Type II Seesaw Model
We propose a minimal type II seesaw model by introducing only one
right-handed neutrino besides the triplet Higgs to the standard
model. In the usual type II seesaw models with several right-handed neutrinos,
the contributions of the right-handed neutrinos and the triplet Higgs to the CP
asymmetry, which stems from the decay of the lightest right-handed neutrino,
are proportional to their respective contributions to the light neutrino mass
matrix. However, in our minimal type II seesaw model, this CP asymmetry is just
given by the one-loop vertex correction involving the triplet Higgs, even
though the contribution of the triplet Higgs does not dominate the light
neutrino masses. For illustration, the Fritzsch-type lepton mass matrices are
considered.Comment: 5 pages, 4 figures, some points clarified, useful references added,
to appear in Phys. Rev.
Effective continuous model for surface states and thin films of three dimensional topological insulators
Two-dimensional effective continuous models are derived for the surface
states and thin films of the three-dimensional topological insulator (3DTI).
Starting from an effective model for 3DTI based on the first principles
calculation [Zhang \emph{et al}, Nat. Phys. 5, 438 (2009)], we present
solutions for both the surface states in a semi-infinite boundary condition and
in the thin film with finite thickness. An effective continuous model was
derived for surface states and the thin film 3DTI. The coupling between
opposite topological surfaces and structure inversion asymmetry (SIA) give rise
to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum.
Besides, the SIA leads to asymmetric distributions of wavefunctions along the
film growth direction, making some branches in the energy spectra much harder
than others to be probed by light. These features agree well with the recent
angle-resolved photoemission spectra of BiSe films grown on SiC
substrate [Zhang et al, arXiv: 0911.3706]. More importantly, we use the
effective model to fit the experimental data and determine the model
parameters. The result indicates that the thin film BiSe lies in
quantum spin Hall region based on the calculation of the Chern number and the
invariant. In addition, strong SIA always intends to destroy the
quantum spin Hall state.Comment: 12 pages, 7 figures, references are update
Optimal entanglement witnesses based on local orthogonal observables
We show that the entanglement witnesses based on local orthogonal observables
which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504
(2005)] and [O. G\"uhne, M. Mechler, G. T\'oth and P. Adam, Phys. Rev. A 74,
010301 (2006)] in linear and nonlinear forms can be optimized, respectively. As
applications, we calculate the optimal nonlinear witnesses of pure bipartite
states and show a lower bound on the I-concurrence of bipartite higher
dimensional systems with our method.Comment: 6 pages, 1 figure; minor changes, references adde
Theory for high spin systems with orbital degeneracy
High-spin systems with orbital degeneracy are studied in the large spin
limit. In the absence of Hund's coupling, the classical spin model is mapped
onto disconnected orbital systems with spins up and down, respectively. The
ground state of the isotropic model is an orbital valence bond state where each
bond is an orbital singlet with parallel spins, and neighbouring bonds interact
antiferromagnetically. The possible relevance to the transition metal oxides
are discussed.Comment: 4 page, three figures, to appear in Phys. Rev. Let
On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations
We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional parameter space. The element that combines these two techniques is that they both utilize ANOVA expansions to achieve the improvements. The first method is a three-step RB-ANOVA-RB method, aiming at using a combination of reduced basis methods and ANOVA expansions to effectively compress the parameter space without impact the accuracy of the output of interest. This is achieved by first building a low-accuracy reduced model for the full high-dimensional parametric problem. This model is used to recover an approximate ANOVA expansion for the output functional at marginal cost, allowing the estimation of the sensitivity of the output functional to parameter variation and enabling a subsequent compression of the parameter space. A new accurate reduced model can then be constructed for the compressed parametric problem at a substantially lower computational cost than for the full problem. In the second approach we explore the ANOVA expansion to drive an hp reduced basis method. This is initiated by setting up a maximum number of reduced bases that can be afforded during the online stage. If the offline greedy procedure for a given parameter domain converges with equal or less than the maximum bases, the offline algorithm stops. Otherwise, an approximate ANOVA expansion is performed for the output functional. The parameter domain is decomposed into several subdomains where the most important parameters according to the ANOVA expansion are split. The offline greedy algorithms are performed in these parameter subdomains. The algorithm is applied recursively until the offline greedy algorithms converge across all parameter subdomains. We demonstrate the accuracy, efficiency, and generality of these two approaches through a number of test cases
Formation of energy gap in higher dimensional spin-orbital liquids
A Schwinger boson mean field theory is developed for spin liquids in a
symmetric spin-orbital model in higher dimensions. Spin, orbital and coupled
spin-orbital operators are treated equally. We evaluate the dynamic correlation
functions and collective excitations spectra. As the collective excitations
have a finite energy gap, we conclude that the ground state is a spin-orbital
liquid with a two-fold degeneracy, which breaks the discrete spin-orbital
symmetry. Possible relevence of this spin liquid state to several realistic
systems, such as CaVV and NaSbTiO, are discussed.Comment: 4 pages with 1 figur
Updated Values of Running Quark and Lepton Masses
Reliable values of quark and lepton masses are important for model building
at a fundamental energy scale, such as the Fermi scale M_Z \approx 91.2 GeV and
the would-be GUT scale \Lambda_GUT \sim 2 \times 10^16 GeV. Using the latest
data given by the Particle Data Group, we update the running quark and
charged-lepton masses at a number of interesting energy scales below and above
M_Z. In particular, we take into account the possible new physics scale (\mu
\sim 1 TeV) to be explored by the LHC and the typical seesaw scales (\mu \sim
10^9 GeV and \mu \sim 10^12 GeV) which might be relevant to the generation of
neutrino masses. For illustration, the running masses of three light Majorana
neutrinos are also calculated. Our up-to-date table of running fermion masses
are expected to be very useful for the study of flavor dynamics at various
energy scales.Comment: 23 pages, 6 tables, 2 figures; version published in PR
Reduced basis multiscale finite element methods for elliptic problems
In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory behavior ([4, 14]). For uniform rectangular meshes, the local oscillating test functions are represented by a reduced basis method, parameterizing the center of the elements. For triangular elements, we introduce a slightly different approach. By exploring over-sampling of the oscillating test functions, initially introduced to recover a better approximations of the global harmonic coordinate map, we first build the reduced basis on uniform rectangular elements containing the original triangular elements and then restrict the oscillating test function to the triangular elements. These techniques are also generalized to the case where the coefficients dependent on additional independent parameters. The analysis of the proposed methods is supported by various numerical results, obtained on regular and unstructured grids
Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
We propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a assumption of saturation of error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy algorithm. In an improved approach, this is combined with an algorithm in which the train set for the greedy approach is adaptively sparsefied and enriched. A safety check step is added at the end of the algorithm to certify the quality of the basis set. Both these techniques are applicable to high-dimensional problems and we shall demonstrate their performance on a number of numerical examples
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