Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hidden order in bosonic gases confined in one dimensional optical
  lattices   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.

26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci