One-dimensional optical lattices and impenetrable bosons
Abstract
We study the limit of large onsite repulsion of the one-dimensional Bose-Hubbard model at low densities, and derive a strong-coupling effective Hamiltonian. By taking the lattice parameter to zero, the Hamiltonian becomes a continuum model of fermions with attractive interactions. The leading corrections to the internal energy of a hard-core-boson (Tonks) gas as well as the (finite temperature) pair correlations of a strongly interacting Bose gas are calculated. We explore the possibility of realizing, in an optical lattice, a Luttinger liquid with stronger density correlations than the Tonks gas. A quantum phase transition to a charge-density-wave Mott insulator is also discussed.
Keywords
Cite
@article{arxiv.cond-mat/0301167,
title = {One-dimensional optical lattices and impenetrable bosons},
author = {M. A. Cazalilla},
journal= {arXiv preprint arXiv:cond-mat/0301167},
year = {2009}
}
Comments
4 pages. Version accepted for publication in Phys. Rev. A; title changed