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

Abstract

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 ∊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 log2 L (L is the length of a subchain) with the coefficient A ≈ 1/3, which is the same as that of the XY chain in a transverse field without the DM interaction for γ = 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.