Quantum phase transition in the one-dimensional period-two and uniform quantum compass model are studied by using the pseudo-spin transformation method and the trace map method. The exact solutions are presented, the fidelity, the nearest-neighbor ps
eudo-spin entanglement, spin and pseudo-spin correlation functions are then calculated. At the critical point, the fidelity and its susceptibility change substantially, the gap of pseudo-spin concurrence is observed, which scales as $1/N$ (N is system size). The spin correlation functions show smooth behavior around the critical point. In the period-two chain, the pseudo-spin correlation functions exhibit a oscillating behavior, which is absent in the unform chain. The divergent correlation length at the critical point is demonstrated in the general trend for both cases.
In the quasilinear Regge trajectory ansatz, some useful linear mass inequalities, quadratic mass inequalities and quadratic mass equalities are derived for mesons and baryons. Based on these relations, mass ranges of some mesons and baryons are given
. The masses of bc-bar and ss-bar belonging to the pseudoscalar, vector and tensor meson multiplets are also extracted. The J^P of the baryon Xi_cc(3520) is assigned to be 1/2^+. The numerical values for Regge slopes and intercepts of the 1/2^+ and 3/2^+ SU(4) baryon trajectories are extracted and the masses of the orbital excited baryons lying on the 1/2^+ and 3/2^+ trajectories are estimated. The J^P assignments of baryons Xi_c(2980), Xi_c(3055), Xi_c(3077) and Xi_c(3123) are discussed. The predictions are in reasonable agreement with the existing experimental data and those suggested in many other different approaches. The mass relations and the predictions may be useful for the discovery of the unobserved meson and baryon states and the J^P assignment of these states.
In this paper we study the properties of diquarks (composed of $u$ and/or $d$ quarks) in the Bethe-Salpeter formalism under the covariant instantaneous approximation. We calculate their BS wave functions and study their effective interaction with the
pion. Using the effective coupling constant among the diquarks and the pion, in the heavy quark limit $m_Qtoinfty$, we calculate the decay widths of $Sigma_Q^{(*)}$ ($Q=c,b$) in the BS formalism under the covariant instantaneous approximation and then give predictions of the decay widths $Gamma(Sigma_b^{(*)}toLambda_b+pi)$.
