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We present a theoretical study on quantum breathers in a XXZ Heisenberg ferromagnet with the single-ion uniaxial anisotropy on a two-dimensional hexangular lattice. In our work, the full quantum and the semiclassical cases are considered, respectively. For the full quantum case, we find that some isolated two-magnon bands can exist below the free magnon band. Physically, each isolated two-magnon band correspond to a two-magnon bound state, which is the simplest quantum breather state. For the semiclassical case, the analytical form of the discrete breather solution with a line localized structure is obtained by adopting the Glauber's coherent-state representation. Furthermore, the influence of the anisotropy on the properties of quantum breathers is discussed in detail. [ABSTRACT FROM AUTHOR]

Under considering the next-nearest-neighbor interaction, quantum breathers in one-dimensional anisotropy ferromagnetic chains are theortically studied. By introducing the Dyson-Maleev transformation for spin operators, a map to a Heisenberg ferromagnetic spin lattice into an extended Bose-Hubbard model can be established. In the case of a small number of bosons, by means of the numerical diagonalization technique, the energy spectrum of the corresponding extended Bose-Hubbard model containing two bosons is calculated. When the strength of the single-ion anisotropy is enough large, a isolated single band appears. This isolated single band corresponds to two-boson bound state, which is the simplest quantum breather state. It is shown that the introduction of the next-nearest-neighbor interaction will lead to interesting band structures. In the case of a large number of bosons, by applying the time-dependent Hartree approximation, quantum breather states for the system is constructed. In this case, the effect of the next-nearest-neighbor interaction on quantum breathers is also analyzed. [ABSTRACT FROM AUTHOR]