We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.
The isotropic
XY model
(s=1/2) in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of
N segments with
n different exchange interactions and magnetic moments, is exactly solved by introducing the integral Gaussian transformation and the generalized Jordan--Wigner transformation, which reduce the problem to the diagonalization of a finite matrix of
nth order. The quantum transitions induced by the transverse field are determined by analyzing the induced magnetization of the cell and the equation of state. The phase diagrams for the quantum transitions, in the space generated by the transverse field and the interaction parameters, are presented. As expected, the model presents multiple, first- and second-order quantum transitions induced by the transverse field, and it corresponds to an extension of the models recently considered by the authors. Detailed results are also presented, at
T=0, for the induced magnetization and isothermal susceptibility ${\ensuremath{\chi}}_{T}^{zz}$ as a function of the transverse field.