Instability and topological robustness of Weyl semimetals against Coulomb interaction

There is a close connection between various new phenomena in Weyl semimetals and the existence of linear band crossings in the single particle description. We show, by a full self-consistent mean-field calculation, how this picture is modified in the presence of long-range Coulomb interactions. The chiral symmetry breaking occurs at strong enough interactions and the internode interband excitonic pairing channel is found to be significant, which determines the gap-opened band profile varying with interaction strength. Remarkably, in the resultant interacting phase, finite band Chern number jumps in the three-dimensional momentum space are retained, indicating the robustness of the topologically nontrivial features.Comment: 8 pages, 4 figures, accepted by Phys. Rev.

Singular perturbations with multiple poles of the simple polynomials

In this article, we study the dynamics of the following family of rational maps with one parameter: \begin{equation*} f_\lambda(z)= z^n+\frac{\lambda^2}{z^n-\lambda}, \end{equation*} where $n\geq 3$ and $\lambda\in\mathbb{C}^*$. This family of rational maps can be viewed as a singular perturbations of the simple polynomial $P_n(z)=z^n$. We give a characterization of the topological properties of the Julia sets of the family $f_\lambda$ according to the dynamical behaviors of the orbits of the free critical points.Comment: 15 pages, 5 figures, to appear in Qualitative Theory of Dynamical System

Boltzmann approach to spin-orbit-induced transport in effective quantum theories

In model studies of the spin/anomalous Hall effect, effective Hamiltonians often serve as the starting point. However, a complete effective quantum theory contains not only the effective Hamiltonian but also the relation linking the physical observables to the canonical ones. We construct the semiclassical Boltzmann (SB) transport framework in the weak disorder-potential regime directly in the level of the effective quantum theory, and confirm this construction by formulating a generalized Kohn-Luttinger density matrix transport theory also in this level. The link and difference between the present SB theory and previous phenomenological Boltzmann, quantum kinetic and usual Kubo-Streda theories are clarified. We also present the slightly generalized Kubo-Streda formula in the level of the effective quantum theory. In this level, it is the generalized Kubo-Streda formula rather than the usual one that leads to the same physical interpretations as the present SB theory. In the application to a Rashba 2D effective model, a nonzero spin Hall effect important in the case of strong Rashba coupling but neglected in previous theories is found.Comment: 6.5+5 pages, 2 figure

Canonical Form and Separability of PPT States on Multiple Quantum Spaces

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in {\Cb}^{K_1} \otimes {\Cb}^{K_2} \otimes ... \otimes {\Cb}^{K_m} \otimes {\Cb}^N composite quantum systems with rank $N$, from which a sufficient separability condition for these states is presented.Comment: 5 page

Indecomposability of entanglement witnesses constructed from any permutations

Let $n\geq 2$ and $\Phi_{n,t,\pi}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})$ be a linear map defined by $\Phi_{n,t,\pi}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,\pi(i)}AE_{i,\pi(i)}^\dag-A$, where $0\leq t\leq n$, $E_{ij}$s are the matrix units and $\pi$ is a non-identity permutation of $(1,2,\cdots,n)$. Denote by $\{{ F}_s: s=1,2\ldots, k\}$ the set of all minimal cycles of $\pi$ and $l(\pi)=\max\{\# { F}_s: s=1,2,\ldots,k\}$ the length of $\pi$. It is shown that the Hermitian matrix $W_{n,t,\pi}$ induced by $\Phi_{n,t,\pi}$ is an indecomposable entanglement witness if and only if $\pi^2\not={\rm id}$ (the identity permutation) and $0<t\leq\frac{n}{l(\pi)}$. Some new bounded entangled states are detected by such witnesses that cannot be distinguished by PPT criterion, realignment criterion, etc..Comment: 11 page

High-Order Extended Finite Element Methods for Solving Interface Problems

In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and three dimensions. Optimal error estimates in the piecewise $H^1$-norm and in the $L^2$-norm are rigorously proved for both schemes. In particular, we have devised a new parameter-friendly DG-XFEM method, which means that no "sufficiently large" parameters are needed to ensure the optimal convergence of the scheme. To prove the stability of bilinear forms, we derive non-standard trace and inverse inequalities for high-order polynomials on curved sub-elements divided by the interface. All the estimates are independent of the location of the interface relative to the meshes. Numerical examples are given to support the theoretical results

The least eigenvalue of graphs whose complements are unicyclic

A graph in a certain graph class is called minimizing if the least eigenvalue of the adjacency matrix of the graph attains the minimum among all graphs in that class. Bell {\it et al.} have characterized the minimizing graphs in the class of connected graphs of order $n$ and size $m$, whose complements are either disconnected or contain a clique of order at least $n/2$. In this paper we discuss the minimizing graphs of a special class of graphs of order $n$ whose complements are connected and contains exactly one cycle (namely the the class $\mathscr {U}^{c}_{n}$ of graphs whose complements are unicyclic), and characterize the unique minimizing graph in $\mathscr {U}^{c}_{n}$ when $n \geq 20$

Phenomenology analysis of duration inflation for Tachyon field in loop quantum cosmology

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in LQC has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter $\alpha$ of the exponential potential and the initial conditions. To get enough e-folding number, $\alpha$ should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor is continuously growing during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase.Comment: 8 pages, 6 figure

Searching for Singlino-Higgsino Dark Matter in the NMSSM

We study a simplified scenario in the next-to-minimal supersymmetric standard model with a split electroweak spectrum, in which only the singlino and higgsinos are light and other superpartners are decoupled. Serving as a dark matter candidate, a singlino-dominated neutralino $\tilde{\chi}_1^0$ should have either resonant annihilation effects or sizable higgsino components to satisfy the observed relic abundance. The sensitivities of LHC searches and dark matter detection experiments are investigated. With an integrated luminosity of $30 (300) \mathrm{fb}^{-1}$, $3l + E_\mathrm{T} \!\!\!\!\!\!\!/ \;\;\;$and $2l + E_\mathrm{T} \!\!\!\!\!\!\!/ \;\;\;$ searches at the 13 (14) TeV LHC are expected to reach up to $m_{\tilde{\chi}_1^0}\sim 150 (230) \mathrm{GeV}$ and $m_{\tilde{\chi}_2^0,\tilde{\chi}_1^{\pm}}\sim 320 (480) \mathrm{GeV}$. Near future dark matter direct and indirect detection experiments can cover some parameter regions where collider searches lose their sensitivities.Comment: 23 pages, 8 figures. v2:parameter points adde

Exploring Fermionic Dark Matter via Higgs Boson Precision Measurements at the Circular Electron Positron Collider

We study the impact of fermionic dark matter (DM) on projected Higgs precision measurements at the Circular Electron Positron Collider (CEPC), including the one-loop effects on the $e^+e^-\to Zh$ cross section and the Higgs boson diphoton decay, as well as the tree-level effects on the Higgs boson invisible decay. As illuminating examples, we discuss two UV-complete DM models, whose dark sector contains electroweak multiplets that interact with the Higgs boson via Yukawa couplings. The CEPC sensitivity to these models and current constraints from DM detection and collider experiments are investigated. We find that there exist some parameter regions where the Higgs measurements at the CEPC will be complementary to current DM searches.Comment: 30 pages, 14 figures; minor revisions to match the published versio