Regular Article

Haldane insulator in the 1D nearest-neighbor extended Bose-Hubbard model with cavity-mediated long-range interactions

Theoretical Physics, Saarland University, Campus E2.6, 66123 Saarbrücken, Germany

^a e-mail: johannes@lusi.uni-sb.de

Received: 2 March 2020
Received in final form: 15 April 2020
Published online: 3 June 2020

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.