The pairing symmetry of the Hubbard Hamiltonian on a triangle lattice with a nearly-flat low energy band is studied with the determinant quantum Monte Carlo method. We show that the low temperature phase is insulating at half-filling, even for relatively weak interactions. The natures of the spin and pairing correlations upon doping are determined, and exhibit an electron-hole asymmetry. Among the pairing symmetries allowed, we demonstrate that the dominating channels are d-wave, opening the possibility of condensation into an unconventional d x 2 −y 2 + idxy phase, which is characterized by an integer topological invariant and gapless edge states. The results are closely related to the correlated insulating phase and unconventional superconductivity discovered recently in twisted bilayer graphene.

The effect of many-body interaction in curved space is studied based on the extended Bose–Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction as q in the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.

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Based on the Hubbard models, quantum magnetism of topologically-designed graphene nanoribbons (GNRs) is studied using exact numerical simulations. We first study a two-band Hubbard model describing the low-energy topological bands using density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) methods. It is found the spin correlations decay quickly with the distance, and the local moment is extrapolated to zero in the presence of symmetry-breaking terms. The results show that the two-band Hubbard chain is nonmagnetic, which is in contrast to the mean-field calculation predicting a critical interaction for the magnetic transition. We then include the Hubbard interaction to the topological-designed GNRs. For large interactions, the spin correlations keep finite for all distances, and the magnetic order develops. The local moment is extrapolated to almost zero for weak interactions, and begins to increase rapidly from a critical interaction. The estimated critical value is much larger than the realistic value in graphene, and we conclude the experimentally relevant GNRs is nonmagnetic, which is consistent with the experimental results.

Hardcore bosons on honeycomb lattice ribbons with zigzag edges are studied using exact numerical simulations. We map out the phase diagrams of ribbons with different widths, which contain superfluid and insulator phases at various fillings. We show that charge domain walls are energetically favorable, in sharp contrast to the more typical occupation of a set of sites on a single sublattice of the bipartite geometry at ρ = 1 2 filling. This 'self-organized domain wall' separates two charge-density-wave (CDW) regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. Our results provide a concrete context to observe bosonic topological phenomena and can be simulated experimentally using bosonic cold atoms trapped in designed optical lattices.Introduction.-One of the most interesting properties of condensed matter systems is their condensation into ordered low temperature phases, breaking an underlying symmetry of the Hamiltonian. Such phases typically minimize the free energy F ; coexistence of the distinct ordered patterns involves a domain wall, increasing F . Nevertheless, domain walls often exist in practice in experiments (or in simulations) as a consequence of long annealing times. This is especially the case in the presence of disorder which can pin their motion.In addition to being manifest as meta-stable states, domain walls can also arise in other ways.An important example is provided by doping away from the commensurate antiferromagnetic (AF) filling of the cuprate superconductors[1], or the Hubbard and t-J models that describe them [2][3][4]. Dopants do not spread uniformly, but instead form "charge stripes". Across these stripes there is a 'π-phase shift' of the AF order [5]. The up-spin occupied sublattice interchanges across the stripe, realizing a domain wall.In model Hamiltonian studies on 'ladder' geometries using the density matrix renormalization group, the charge patterns are found to be 'vertical stripes', i.e. the doped holes lie parallel to the short direction of the cluster [3]. These charge patterns are fundamentally connected not only to magnetism, e.g. the π phase shift, but also to charge density wave and d-wave pairing order. Studies of stripe physics and the associated domain walls remain of great interest [6,7], with the possible coexistence of Luther-Emery liquid states in which the spin excitations are gapped, and quasi-long range superconducting correlations being a key issue [8].In this Letter we study bosonic particles on honeycomb ribbons. We discuss four novel features of this geometry.