Dipole-monopole criticality and chargeless half mode in an integrable gauge-coupled pseudoexciton-phonon system on a...

A one-dimensional nonlinear dynamical system of gauge-coupled intrasite excitations and lattice vibrations on an infinite one-dimensional regular lattice is studied. The system as a whole is shown to be integrable in the Lax sense and it admits the exact four-component analytical solutions. Two mutually PT-conjugated symmetry broken solutions are explicitly isolated in the framework of the Darboux-Bäcklund dressing technique. Each of the obtained four-component solutions demonstrates the pronounced interplay between the interacting subsystems in the form of an essentially nonlinear superposition of two principally distinct types of traveling waves characterized by two physically distinct spatial scales and by two distinct running velocities. Depending on the relationships between the spatial scaling parameters the system can manifest itself in three qualitatively distinct dynamical regimes referred to as the monopole regime, dipole regime, and threshold regime. The threshold value of the localization parameter separating the monopole and dipole dynamical regimes is strictly established in terms of basic physical parameters. The phenomenon of dipole-monopole crossover for the spatial distribution of pseudoexcitons is shown to initiate the partial splitting between the pseudoexcitonic and vibrational subsystems in the threshold dynamical regime specified by the threshold value of the localization parameter. This partial splitting is manifested by the complete elimination of one pseudoexcitonic component accompanied by the actual conversion of another pseudoexcitonic component into a pseudoexcitonic chargeless half mode. The integrable nonlinear pseudoexciton-phonon system under study is expected to be applicable for modeling the nonlinear dynamical properties of properly designed PT-symmetric metamaterials.