Hidden order in bosonic gases confined in one-dimensional optical lattices
Authors: Amico L., Mazzarella G., Pasini S., Cataliotti F.S.
Autors Affiliation: MATIS-INFM, Dipartimento di Metodologie Fisiche e Chimiche (DMFCI), Universitá di Catania, viale A. Doria 6, 95125 Catania, Italy; Dipartimento di Fisica \’G. Galilei\’, CNISM, Universita Degli Studi di Padova, via F. Marzolo 8, 35131 Padova, Italy; Lehrstuhl für Theoretische Physik I, Technische Universität Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany; Dipartimento di Energética, LENS, Universitá di Firenze, via N. Carrara 1, 50019 Firenze, Italy
Abstract: 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 one-dimensional (1D) optical lattice. For certain constraints between the coupling constants, we construct an explicit relationship between such an effective bosonic Hamiltonian and the integrable spin-5 anisotropic Heisenberg model. The former results are therefore integrable by construction. The field theory is governed by an anisotropic nonlinear s-model with singlet and triplet massive excitations; this 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 sheds light on the hidden symmetry of the Haldane type for ID bosons.
Journal/Review: NEW JOURNAL OF PHYSICS
Volume: 12 Pages from: 013002 to: 013002
More Information: We thank M A Martin-Delgado, A Pronko, A Sedrakyian, G Sierra and F Sols for very useful discussions. LA acknowledges support from MEC (FIS2007-65723); FSC acknowledges support from the EU through project CHIMONO; GM acknowledges support from \’Fondazione CARIPARO\’.KeyWords: Anisotropic Heisenberg models; Bosonic atoms; Bosonic systems; Coupling constants; Effective Hamiltonian; Field theory; Haldane; Hidden Order; Hidden symmetry; One dimensional optical lattice; Optical lattices; Overlap integrals; Power series expansions; Wannier functions, Anisotropy; Chemical bonds; Hamiltonians; Molecular orbitals; Optical materials; Particle optics; Phase diagrams; Wave functions, Crystal latticesDOI: 10.1088/1367-2630/12/1/013002