Hidden order in bosonic gases confined in one dimensional optical lattices

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 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.

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

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• Entanglement Spectroscopy using Quantum Monte Carlo
• Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture
• Nontrivial Haldane phase of an atomic two-component Fermi gas trapped in a 1d optical lattice
• Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species
• Modulational instabilities in lattices with power-law hoppings and interactions
• Superfluid phases induced by the dipolar interactions
• On the spin-liquid phase of one dimensional spin-1 bosons
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Quantum phases of dipolar bosons in one-dimensional optical lattices
• Quantum phases in $p$-orbital degenerated attractive 1D fermionic optical lattices
• Strongly Interacting Two-component Coupled Bose Gas in Optical Lattices
• Kondo Length in Bosonic Lattices