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

Bernd Schmidt, Michael Bortz, Sebastian Eggert, Michael Fleischhauer, and David Petrosyan
Phys. Rev. A 79, 063634 – Published 30 June 2009

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 intersite 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 (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that 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 methods.

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  • Received 27 February 2009

DOI:https://doi.org/10.1103/PhysRevA.79.063634

©2009 American Physical Society

Authors & Affiliations

Bernd Schmidt, Michael Bortz, Sebastian Eggert, and Michael Fleischhauer

  • Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, D-67663 Kaiserslautern, Germany

David Petrosyan

  • Institute of Electronic Structure and Laser, FORTH, 71110 Heraklion, Crete, Greece

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Issue

Vol. 79, Iss. 6 — June 2009

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