Random-Phase-Approximation Excitation Spectra for Bose-Hubbard Models

• Published in: arXiv.org 2014-10
• Main Authors: Jamshid Moradi Kurdestany, Pai, Ramesh V, Pandit, Rahul
• Format: Article
• Language: English
• Subjects: Acoustic velocity; Approximation; Bosons; Couplings; Dependence; Excitation spectra; Mean field theory; Phase transitions; Phases
• ISSN: 2331-8422

We obtain the excitation spectra of the following three generalized Bose-Hubbard (BH) models: (1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH) for spinless interacting bosons of one species. In all the phases of these models we provide a unified treatment of random-phase-approximation (RPA) excitation spectra. These spectra have gaps in all the MI phases and gaps in the DW phases in the EBH model; they are gapless in all the SF phases in these models and in the SS phases in the EBH model. We obtain the dependence of (a) gaps \(\Delta\) and (b) the sound velocity \(u_s\) on the parameters of these models and examine \(\Delta\) and \(u_s\) as these systems go through phase transitions. At the SF-MI transitions in the spin-1 BH model, \(u_s\) goes to zero continuously (discontinuously) for MI phases with an odd (even) number of bosons per site; this is consistent with the natures of these transition in mean-field theory. In the SF phases of these models, our excitation spectra agree qualitatively, at weak couplings, with those that can be obtained from Gross-Pitaevskii-type models. We compare the results of our work with earlier studies of related models and discuss implications for experiments.