The effects of the Dzyaloshinskii-Moriya interaction on the ground-state properties of the XY chain in a transverse field

The effects of the Dzyaloshinski-Moriya (DM) interaction on the ground-state properties of the anisotropic XY chain in a transverse field have been studied by means of correlation functions and entanglement. Different from the case without the DM interaction, the excitation spectra epsilon(k) of this model are not symmetrical in the momentum space and are not always positive. As a result, besides the ferromagnetic (FM) and the paramagnetic (PM) phases, a gapless chiral phase is induced. In the chiral phase, the von Neumann entropy is proportional to log(2)L (L is the length of a subchain) with the coefficient A approximate to 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for gamma = 0 and 0 < h <= 1. And in the vicinity of the critical point between the chiral phase and the FM (or PM) phase, the behaviors of the nearest-neighbor concurrence and its derivative are like those for the anisotropy transition.