Quantum signature of discrete breathers in a nonlinear Klein–Gordon lattice with nearest and next-nearest neighbor interactions

•Both semiclassical and quantum descriptions of breathers are considered.•The effect of the long-range interaction is investigated.•The semiclassical analytical solutions of discrete breathers are gotten.•The energy spectrum of the system containing two quanta is calculated.

A theoretical work on quantum breathers in a nonlinear Klein–Gordon lattice model with nearest and next-nearest neighbor interactions is presented. The semiclassical and the full quantum cases are respectively considered. For the semiclassical case, we obtain the analytical solution of discrete breather, and find that the wave number corresponding to the appearance of discrete breather changes when the ratio of the next-nearest- to -nearest - neighbor harmonic force constants is greater than 1/4. For the full quantum case, by calculating the energy spectrum of the system containing two quanta, we prove numerically the existence of quantum breathers (two-quanta bound states) and find the shape of energy spectrum changes dramatically as the value of next -nearest neighbor harmonic force constant increasing.