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arXiv · 0902.4442

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

Bernd Schmidt·Michael Bortz·Sebastian Eggert·Michael Fleischhauer·David Petrosyan
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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.

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Bernd Schmidt, Michael Bortz, Sebastian Eggert, Michael Fleischhauer, David Petrosyan. 2009-02-25. Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism. https://doi.org/10.1103/physreva.79.063634

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