Haldane insulator in the 1D nearest-neighbor extended Bose-Hubbard model with cavity-mediated long-range interactions
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Haldane insulator in the 1D nearest-neighbor extended BoseHubbard model with cavity-mediated long-range interactions Johannes Sicks a and Heiko Rieger Theoretical Physics, Saarland University, Campus E2.6, 66123 Saarbr¨ ucken, Germany
Received 2 March 2020 / Received in final form 15 April 2020 Published online 3 June 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com
Abstract. In the one-dimensional Bose-Hubbard model with on-site and nearest-neighbor interactions, a gapped phase characterized by an exotic non-local order parameter emerges, the Haldane insulator. Bose-Hubbard models with cavity-mediated global range interactions display phase diagrams, which are very similar to those with nearest-neighbor repulsive interactions, but the Haldane phase remains elusive there. Here we study the one-dimensional Bose-Hubbard model with nearest-neighbor and cavity-mediated global-range interactions and scrutinize the existence of a Haldane Insulator phase. With the help of extensive quantum Monte-Carlo simulations we find that in the Bose-Hubbard model with only cavity-mediated global-range interactions no Haldane phase exists. For a combination of both interactions, the Haldane Insulator phase shrinks rapidly with increasing strength of the cavity-mediated global-range interactions. Thus, in spite of the otherwise very similar behavior the mean-field like cavity-mediated interactions strongly suppress the non-local order favored by nearest-neighbor repulsion in some regions of the phase diagram.
1 Introduction For several decades, the Bose-Hubbard model (BHM) [1] has attracted continued interest. In its most simplistic form, it exhibits two phases in the ground state: a Mott insulator (MI) phase and a superfluid (SF) phase, depending if on-site repulsion or nearest-neighbor hopping dominates. Through the years, quantum Monte-Carlo (QMC) methods contributed greatly to the investigation of quantum critical phenomena. Here, one must especially emphasize path-integral Monte-Carlo [2,3], world-line QMC [4,5], worm-algorithm QMC [6–9] and, as a derivative, the stochastic Green’s function algorithm [10,11]. Also approximate techniques were applied to the BHM, like mean-field theory [1,12,13], strong coupling expansion [14], Gutzwiller wave function variational calculation [15, 16] and density matrix renormalisation group method [17]. First experimental realizations of the BHM involved ultracold bosons trapped in optical lattices [18,19] and initiated studies of many-body bosonic gases with additional potentials and interactions [20–22]. These extended models generally feature new phases [23–28]. Analyzing extended models, several inclusions to the BHM were made, e.g. the addition of harmonic confining potentials [29,30], three-body interactions [31], disordered potentials [32–34], long-range dipolar interactions [26,35], nearest-neighbor interactions [17,23,27,28,36– 40], next-nearest-neighbor interactions [5,41–43], a
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