Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism

TL;DR

This paper studies a lattice system of bound bosonic atom pairs, revealing complex phase behavior including antiferromagnetic order, and employs analytical and numerical methods to characterize correlations and phases.

Contribution

It introduces an effective model for bound atom pairs in the Bose-Hubbard system and analyzes its phase diagram and correlations using Bethe Ansatz, DMRG, and perturbation theory.

Findings

Identification of incompressible and antiferromagnetic phases

Exact calculation of Luttinger parameter K

Excellent agreement between analytical and numerical correlation results

Abstract

We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the inter-site tunneling rate. An ensemble of such lattice-dimers is accurately described by an effective Hamiltonian of hard core bosons with strong nearest-neighbor repulsion which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (anti-ferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the anti-ferromagnetic density profile and in density-density correlations. We derive a kink model which provides simple quantitative explanation of these features. To describe the long-range correlations of the system we employ the Luttinger liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe Ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density matrix renormalization group (DMRG) methods. We also present a perturbative treatment of the system in higher dimensions.