Hidden order in bosonic gases confined in one dimensional optical lattices

TL;DR

This paper explores the hidden order in one-dimensional bosonic gases in optical lattices by linking their effective Hamiltonian to integrable spin models and analyzing their phase diagram and critical behavior.

Contribution

It establishes a relation between the effective bosonic Hamiltonian and the integrable spin-$S$ anisotropic Heisenberg model, revealing hidden symmetries and critical properties.

Findings

Effective Hamiltonian is related to integrable spin model.

The system exhibits a Haldane-type hidden symmetry.

A schematic phase diagram of the bosonic system is proposed.

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.