Nematic state stabilized by off-site Coulomb interaction in iron-based superconductors

Using a variational Monte Carlo method, we investigate the nematic state in iron-base superconductors based on a three-band Hubbard model. Our results demonstrate that the nematic state, formed by introducing an anisotropic hopping order into the projected wave function, can arise in the underdoped regime when a realistic off-site Coulomb interaction $V$ is considered. {\color {red} We demonstrate that the off-site Coulomb interaction $V$, which is neglected so far in the analysis of iron-base superconductors, make a dominant contribution to the stabilization of nematic state. We calculate the doping dependencies of the anisotropic properties such as the unequal occupation of $d_{xz}$ and $d_{yz}$ orbitals, anisotropies of kinetic energy and spin correlations, and show that they are all suppressed upon electron doping, which are consistent with the intrinsic anisotropies observed by optical spectrum measurement and ARPES experiments.Comment: 5 pages, 4 figure

Band-filling and correlation controlling electronic properties and magnetism in Kx_{x}Fe2−y_{2-y}Se2_{2}: A slave boson study

In this paper we investigate the electronic and magnetic properties of K$_{x}$Fe$_{2-y}$Se$_{2}$ materials at different band fillings utilizing the multi-orbital Kotliar-Ruckenstein's slave-boson mean field approach. We find that at three-quarter filling, corresponding to KFe$_{2}$Se$_{2}$, the ground state is a paramagnetic bad metal. Through band renormalization analysis and comparison with the angle-resolved photoemission spectra data, we identify that KFe$_{2}$Se$_{2}$ is also an intermediate correlated system, similar to iron-pnictide systems. At two-third filling, corresponding to the Fe$^{2+}$-based systems, the ground state is a striped antiferromagnetic (SAFM) metal with spin density wave gap partially opened near the Fermi level. In comparison, at half filling case, corresponding to the Fe$^{3+}$-based compounds, besides SAFM, a $N\acute{e}el$ antiferromagnetic metallic ground state without orbital ordering is observed in the intermediate correlation range, and an orbital selective Mott phase (OSMP) accompanied with an intermediate-spin to high-spin transition is also found. These results demonstrate that the band filling and correlation control the electronic state, Fermi surface topology and magnetism in K$_{x}$Fe$_{2-y}$Se$_{2}$.Comment: 21 pages, 12 figure

Coexistence of localized and itinerant magnetism in newly discovered iron-selenide superconductor LiFeO2Fe2Se2

The electronic structure and magnetism of LiFeO$_{2}$Fe$_{2}$Se$_{2}$ are investigated using the first-principle calculations. The ground state is N$\acute{e}$el antiferromagnetic (AFM) Mott insulating state for Fe1 with localized magnetism in LiFeO$_{2}$ layer and striped AFM metallic state for Fe2 with itinerant magnetism in Fe$_{2}$Se$_{2}$ layer, accompanied with a weak interlayer AFM coupling between Fe1 and Fe2 ions, resulting in a coexistence of localized and itinerant magnetism. Moreover, the layered LiFeO$_{2}$ is found to be more than an insulating block layer but responsible for enhanced AFM correlation in Fe$_{2}$Se$_{2}$ layer through the interlayer magnetic coupling. The interplay between the magnetisms of Fe1 and Fe2 introduces a control mechanism for spin fluctuations associated with superconductivity in iron-based superconductors.Comment: 5 pages, 7 figure

Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement

Tsallis-$q$ entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for $q$ tending to 1. We first expand the range of $q$ for the analytic formula of Tsallis-\emph{q} entanglement. For \frac{5-\sqrt{13}}{2} \leq \emph{q} \leq \frac{5+\sqrt{13}}{2}, we prove the monogamy relation in terms of the squared Tsallis-$q$ entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-$q$ entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the $\mu$-th power of Tsallis-\emph{q} entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.Comment: This paper was submitted on 27th Marc

External Shock in a Multi-Bursting Gamma-ray Burst: Energy Injection Phase induced by the Later Launched Ejecta

Central engine of gamma-ray bursts (GRBs) may be intermittent and launch several episodes of ejecta separated by a long quiescent interval. In this scenario, an external shock is formed due to the propagation of the first launched ejecta into the circum-burst medium and the later launched ejecta may interact with the external shock at later period. Owing to the internal dissipation, the later launched ejecta may be observed at a later time ($t_{\rm{jet}}$). In this paper, we study the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$, where $t_{\rm{b}}$ is the collision time of the later launched ejecta with the formed external shock. It is found that the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$ depends on the bulk Lorentz factor ($\Gamma_{\rm{jet}}$) of the later launched ejecta and the density ($\rho$) of the circum-burst medium. If the value of $\Gamma_{\rm{jet}}$ or $\rho$ is low, the $t_{\rm{b}}$ would be significantly larger than $t_{\rm{jet}}$. However, the $t_{\rm{b}}\sim t_{\rm{jet}}$ can be found if the value of $\Gamma_{\rm{jet}}$ or $\rho$ is significantly large. Our results can explain the large lag of the optical emission relative to the $\gamma$-ray/X-ray emission in GRBs, e.g., GRB~111209A. For GRBs with a precursor, our results suggest that the energy injection into the external shock and thus more than one external-reverse shock may appear in the main prompt emission phase. According to our model, we estimate the Lorentz factor of the second launched ejecta in GRB~160625B.Comment: 10 pages, 4 figures, accepted for publication in Ap

Steep Decay Phase Shaped by the Curvature Effect. II. Spectral Evolution

We derive a simple analytical formula to describe the evolution of spectral index $\beta$ in the steep decay phase shaped by the curvature effect with assumption that the spectral parameters and Lorentz factor of jet shell is the same for different latitude. Here, the value of $\beta$ is estimated in 0.3$-$10keV energy band. For a spherical thin shell with a cutoff power law (CPL) intrinsic radiation spectrum, the spectral evolution can be read as a linear function of observer time. For the situation with Band function intrinsic radiation spectrum, the spectral evolution may be complex. If the observed break energy of radiation spectrum is larger than 10keV, the spectral evolution is the same as that shaped by jet shells with a CPL spectrum. If the observed break energy is less than 0.3keV, the value of $\beta$ would be a constant. Others, the spectral evolution can be approximated as a logarithmal function of the observer time in generally.Comment: 24 pages, 13 figures, accepted for publication in Ap

The Feasibility and Flexibility of Selecting Quasars by Variability Using Ensemble Machine Learning Algorithms

In this work we train three decision-tree based ensemble machine learning algorithms (Random Forest Classifier, Adaptive Boosting and Gradient Boosting Decision Tree respectively) to study quasar selection in the variable source catalog in SDSS Stripe 82. We build training and test samples (both containing 1:1 of quasars and stars) using the spectroscopic confirmed sources in SDSS DR14 (including 8330 quasars and 3966 stars). We find that, trained with variation parameters alone, all three models can select quasars with similarly and remarkably high precision and completeness ($\sim$ 98.5% and 97.5%), even better than trained with SDSS colors alone ($\sim$ 97.2% and 96.5%), consistent with previous studies. Through applying the trained models on the variable sources without spectroscopic identifications, we estimate the spectroscopically confirmed quasar sample in Stripe 82 variable source catalog is $\sim$ 93% complete (95% for $m_i<19.0$). Using the Random Forest Classifier we derive the relative importance of the observational features utilized for classifications. We further show that even using one- or two-year time domain observations, variability-based quasar selection could still be highly efficient.Comment: 20 pages, 13 figures, accepted to RA

Steep Decay Phase Shaped by the Curvature Effect. I. Flux Evolution

The curvature effect may be responsible for the steep decay phase observed in gamma-ray bursts. For testing the curvature effect with observations, the zero time point $t_0$ adopted to plot observer time and flux on a logarithmic scale should be appropriately selected. In practice, however, the true $t_0$ cannot be directly constrained from the data. Then, we move $t_0$ to a certain time in the steep decay phase, which can be easily identified. In this situation, we derive an analytical formula to describe the flux evolution of the steep decay phase. The analytical formula is read as $F_\nu\propto (1+\tilde t_{\rm obs}/{\tilde t_c})^{-\alpha}$ with $\alpha(\tilde{t}_{\rm obs})=2+{\int_{0}^{\log (1+\tilde{t}_{\rm obs}/{\tilde{t}_c})} {\beta(\tau)d[\log(1+\tau/{\tilde{t}_c})]}}/{\log (1 + {\tilde t}_{\rm obs}/{{\tilde t}_c})}$, where $F_\nu$ is the flux observed at frequency $\nu$, $\tilde t_{\rm obs}$ is the observer time by setting zero time point $t_0$ at a certain time in the steep decay phase, $\beta$ is the spectral index estimated around $\nu$, and ${\tilde t}_c$ is the decay timescale of the phase with $\tilde{t}_{\rm obs}{\geqslant}0$. We test the analytical formula with the data from numerical calculations. It is found that the analytical formula presents a well estimation about the evolution of flux shaped by the curvature effect. Our analytical formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase.Comment: 28 pages, 18 figures, accepted for publication in Ap

Polygamy relation for the R\'enyi-α\alpha entanglement of assistance in multi-qubit systems

We prove a new polygamy relation of multi-party quantum entanglement in terms of R\'{e}nyi-$\alpha$ entanglement of assistance for $\left( {\sqrt 7 - 1} \right)/2\leq\alpha \leq \left( {\sqrt 13 - 1} \right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since R\'{e}nyi-$\alpha$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $\mu$th power of R\'{e}nyi-$\alpha$ entanglement of assistance.Comment: 6 pages, 7 figure

Correlations of Disk and Jet Emission Deviating from the Fundamental Plane

The variability of accretion rate, which is believed to induce the aperiodic variability of X-ray emission from disk, may affect the energy injection into the jet. In this spirit, a correlation between disk emission and jet emission can be formed even if the mean luminosity of disk emission keeps constant. In this work, these correlations are found in the situation that the luminosity of disk emission is variable and kept with a constant mean value. The obtained correlations may be shallower than that of the fundamental plane of black hole activity. In addition, the slope of correlation may increase with increasing observed frequency of jet emission. For the luminosities spacing with three days, the slope of correlation decreases with increasing black hole mass. The deviation of our found correlations from that of the fundamental plane is related to the suppression of variability in the jet emission in comparison with that in the disk emission. This mechanism may work in some sources in which shallower correlations have been reported. Moreover, it implies that luminosities used to estimate the relation of fundamental plane should cover an appropriate timescale, in which the variability of jet emission is not significantly suppressed.Comment: 19 pages, 5 figures, accepted for publication in Ap