Quantum breathers and modulational instability in quantum zigzag spin chains with alternative combination ferromagnetic and antiferromagnetic interactions in an external magnetic field

Quantum breathers properties and modulational instability in quantum zigzag spin chains with alternative combination ferro-antiferromagnetic interactions are carried out. For a few number of bosons, by using the number states method and numerical diagonalization, the energy spectrum, multi-quantum breathers states and theirs new properties are found. For a large number of bosons, based on the time dependent Hartree approximation and semi-discrete multiple-scale method, we provide a detailed analytical analysis, discuss conditions to obtain solitons bright localized solutions and predict the formation of instability regions in the system. In both configurations, we have constructed quantum breathers states and deduced their quantum energies. Furthermore the modulational instability analysis are done and the formation conditions of appearance instabilities regions predicted by our analytical investigations are found and are in full agreement. Convincing quantitative agreement has been found between the analytical approaches and the numerical simulations for the modulational instability. Experimental data on Rb2Cu2Mo3O12 are parameters used in this work.