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-inte
ger 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 $t_x eq t_y$ 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.
Determinant Quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters -a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping $t$ and on-site r
epulsion $U$ coupled by an inter-plaquette hopping $t leq t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For $U/t=4$, DQMC indicates an optimal $t/t approx 0.4$ at which the pairing vertex is most attractive. The optimal $t/t$ increases with $U/t$. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO$_2$ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.
The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a `checkerboard charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a su
persolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $hat x$ and $hat y$ directions, we conclude that phase separation still occurs.
Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO_2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two dimensional Hubb
ard Hamiltonian. In this paper we use determinant Quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the d-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearence of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a pi-phase shift in the magnetic order.
