Charge Gaps at Fractional Fillings in Boson Hubbard Ladders

Abstract

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 non-integer 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 $t_x\ne t_y$ in the bosonic hopping, extending the work of Crepin {\it 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.

8 pages, 15 figures

References in corpus (7)

• Monte Carlo study of two-dimensional Bose-Hubbard model
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator - Luttinger liquid - Bose glass
• Quantum phases of bosons in double-well optical lattices
• Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices
• Cell strong coupling perturbative approach to the phase diagram of ultracold bosons in optical superlattices
• Fractional-filling Mott domains in two dimensional optical superlattices