Hidden order in bosonic gases confined in one dimensional optical lattices

Details Hidden order in bosonic gases confined in one dimensional optical lattices Hidden order in bosonic gases confined in one dimensional optical lattices

2008-06-14

arxiv.org/abs/0806.2378v3

New J.Phys.12:013002,2010

Physics

Condensed Matter

Other Condensed Matter

5 pages; 1 eps figure. Revised version, to be published in New. J. Phys

Scientific paper

10.1088/1367-2630/12/1/013002

We analyze the effective Hamiltonian arising from a suitable power series expansion of the overlap integrals of Wannier functions for confined bosonic atoms in a 1d optical lattice. For certain constraints between the coupling constants, we construct an explicit relation between such an effective bosonic Hamiltonian and the integrable spin-$S$ anisotropic Heisenberg model. Therefore the former results to be integrable by construction. The field theory is governed by an anisotropic non linear $\sigma$-model with singlet and triplet massive excitations; such a result holds also in the generic non-integrable cases. The criticality of the bosonic system is investigated. The schematic phase diagram is drawn. Our study is shedding light on the hidden symmetry of the Haldane type for one dimensional bosons.

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