Abstract
A theoretical work on modulational instability and quantum local breather modes in a one-dimensional easy-axis Heisenberg ferromagnetic spin lattice with the Dzyaloshinskii-Moriya interaction is completed in the Hartree approximation. By means of the discrete modulational instability analysis, we discuss the influence of the Dzyaloshinskii-Moriya interaction on modulational instability regions and predict the presence condition for the bright stationary localized solution. We find that that the region of the modulational instability moves to the left of the Brillouin zone because of the introduction of the Dzyaloshinskii-Moriya interaction, which is a new finding. Moreover, we get the analytical bright stationary localized solution and analyze the influence of the on-site easy-axis anisotropy and the Dzyaloshinskii-Moriya interaction on their appearance conditions. By the use of such bright stationary localized single-boson wave functions, we construct the quantum breather state that has obvious quantum properties. In addition, the role of the easy-axis anisotropy and the Dzyaloshinskii-Moriya interaction on quantum breather modes is discussed.
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