Spin Ferroquadrupolar Order in the Nematic Phase of FeSe

We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitatively consistent result with inelastic neutron scattering experiments on FeSe at both low and high energies. We verify that FQ can coexist with $C_4$ breaking environments in the mean-field calculation, and further discuss the possibility that quantum fluctuations in FQ act as a source of nematicity.Comment: 8 pages, 7 figures, Erratum adde

Unified Spin Model for Magnetic Excitations in Iron Chalcogenides

Recent inelastic neutron scattering (INS) measurements on FeSe and Fe(Te$_{1-x}$Se$_x$), have sparked intense debate over the nature of the ground state in these materials. Here we propose an effective bilinear-biquadratic spin model which is shown to consistently describe the evolution of low-energy spin excitations in FeSe, both under applied pressure and upon Se/Te substitution. The phase diagram, studied using a combination of variational mean-field, flavor-wave calculations, and density-matrix renormalization group (DMRG), exhibits a sequence of transitions between the columnar antiferromagnet common to the iron pnictides, the non-magnetic ferroquadrupolar phase attributed to FeSe, and the double-stripe antiferromagnetic order known to exist in Fe$_{1+y}$Te. The calculated spin structure factor in these phases mimics closely that observed with INS in the Fe(Te$_{1-x}$Se$_x$), series. In addition to the experimentally established phases, the possibility of incommensurate magnetic order is also predicted.Comment: 9 pages, 10 figures in the main text; plus 5 pages of supplementary material

Dynamical Mean Field Theory for the Bose-Hubbard Model

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.Comment: 11 pages, 8 figure

DEFINITION AND CONSTRUCTION OF THE CORE COMPETENCE IN REAL ESTATE INDUSTRY

The real estate is a very high risk profession. Its funds devotion is big, the operation period is long and the market change quickly. At the same time, the real estate has to face the high level competition that brought by international capital investment. The key to deal with these problems is how to set up and enhance the core competence of the real estate industry while integrating the strategic resources. In this paper we will analyze the features of core competence, thus define the core competence in real estate Industry. The main competition factors of real estate industry include land resources, capital scale and market management. Accordingly, we put forward the solution to establish the core competence of real estate industry. Key words: Core competence, Real estate, Investmen

Spin liquid nature in the Heisenberg J1J_{1}-J2J_{2} triangular antiferromagnet

We investigate the spin-$\frac{1}{2}$ Heisenberg model on the triangular lattice in the presence of nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015); Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015)], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime $0.08\lesssim J_2/J_1\lesssim 0.16$, framed by $120^{\circ}$ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) $J_2/J_1$. By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless $U(1)$ Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped $\mathbb{Z}_{2}$ spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error-bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test-bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.Comment: Editors' Suggestion. 16 pages, 13 figures, 4 table

Variational Monte Carlo study of gapless spin liquid in the spin-1/21/2 XXZ antiferromagnetic model on the kagome lattice

By using the variational Monte Carlo technique, we study the spin-$1/2$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids (with $U(1)$ or $Z_2$ symmetry) or magnetically ordered phases (with ${\bf q}=(0,0)$ or ${\bf q}=(4\pi/3,0)$). We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U(1)$ to $Z_2$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U(1)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.Comment: 7 pages, 7 figure