Bosonic Hofstadter butterflies in the presence of phonon modes

Abstract

Abstract We have investigated the influence of lattice sites vibrations on bosonic Hofstadter’s butterfly (HB) spectrum for the case of conventional square lattice. Only the pair of specific phonon modes with opposite quasimomenta has been taken into account. The study has shown that HB-type spectra can be substantially modified by the presence of phonons, depending on the ratios of such parameters of the system as site-to-site transition amplitudes, particle-phonon interaction constant, and characteristic vibration frequency.