Charge gaps at fractional fillings in boson Hubbard ladders

The Bose-Hubbard Hamiltonian describes the competition between superfluidity and Mott insulating behavior at zero temperature and commensurate filling as the strength of the on-site repulsion is varied. Gapped insulating phases also occur at noninteger densities as a consequence of longer ranged repulsive interactions. In this paper we explore the formation of gapped phases in coupled chains due instead to anisotropies t(x) not equal t(y) in the bosonic hopping, extending the work of Crepin et al. [Phys. Rev. B 84, 054517 (2011).] on two coupled chains, where a gap was shown to occur at half filling for arbitrarily small interchain hopping t(y). Our main result is that, unlike the two-leg chains, for three- and four-leg chains, a charge gap requires a finite nonzero critical t(y) to open. However, these finite values are surprisingly small, well below the analogous values required for a fermionic band gap to open.