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arXiv:2002.12697 · The European Physical Journal B

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

Johannes Sicks, Heiko Rieger

Published Jun 1, 2020• 8 citations
arXivHTMLPDF

Abstract

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. Graphical abstract

DOI
10.1140/epjb/e2020-10109-3

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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. Graphical abstract
We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte-Carlo simulations. We show that when the intra-well repulsion is as strong as the on-site repulsion a dimerized Mott insulator phase appears at the tip of the dimerized Density Wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
We consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte Carlo simulations. We show that when the intrawell repulsion is as strong as the on-site repulsion, a dimerized Mott-insulator phase appears at the tip of the dimerized density-wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane-insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
Abstract Recent experiments with ultracold atoms in an optical lattice have realized cavity-mediated long-range interaction and observed the emergence of a supersolid phase and a density wave phase in addition to Mott insulator and superfluid phases. Here we consider theoretically the effect of uncorrelated disorder on the phase diagram of this system and study the two-dimensional Bose-Hubbard model with cavity-mediated long-range interactions and uncorrelated diagonal disorder. We also study the phase diagram of the extended Bose-Hubbard model with nearest-neighbor interactions in the presence of uncorrelated diagonal disorder. The extended Bose-Hubbard model with nearest-neighbor interactions has been realized in the experiment using dipolar interaction recently. With the help of quantum Monte Carlo simulations using the worm algorithm, we determine the phase diagram of those two models. We compare the phase diagrams of cavity-mediated long-range interactions with nearest-neighbor interactions. We show that two kinds of Bose glass phases exist: one with and one without density wave order. We also find that weak disorder enhances the supersolid phase. Graphical abstract
The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.
By means of the density matrix renormalization group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose–Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region, we are able to distinguish between the conventional Mott insulating and density-wave phases and the Haldane insulator phase displaying long-range string ordering, as originally predicted by Dalla Torre et al (2006 Phys. Rev. Lett. 97 260401).
We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The quantum phase transitions between the different insulating phases were determined from the central charge via the von Neumann entropy. The Haldane phase reveals a characteristic fourfold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain.