One-dimensional Bose-Hubbard model with local three-body interactions

Abstract

We employ the (dynamical) density matrix renormalization group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes t and local two-body and three-body repulsion of strength U and W, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in t/(U+W), even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.

revised version, 7 pages, 5 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Tomonaga-Luttinger parameters for doped Mott insulators
• Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model
• Tomonaga-Luttinger-liquid criticality: numerical entanglement entropy approach
• Exact diagonalization of the one dimensional Bose-Hubbard model with local 3-body interactions
• Three body on-site interactions in ultracold bosonic atoms in optical lattices and superlattices

Cited by in corpus (10)

• Non-standard Hubbard models in optical lattices: a review
• Two-body repulsive bound pairs in multi-body interacting Bose-Hubbard model
• Criticality in the Bose-Hubbard model with three-body repulsion
• One-dimensional Bose-Hubbard model with pure three-body interactions
• Quantum phases of hardcore bosons in two coupled chains: A density matrix renormalization group study
• Three-body interacting dipolar bosons and the fate of lattice supersolidity
• Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator
• Mott insulator phases of non-locally coupled bosons in bilayer optical superlattices
• Spin-1 Bose-Hubbard model with two- and three-body interactions
• Dynamical symmetry in quantum dissipative models