Self-organized bosonic domain walls

Abstract

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.

Hardcore bosonic domain walls on honeycomb lattice

“…Next we study the topological property of the Bose-Hubbard model with a uniform staggered potential on a lattice with periodic boundary condition in both directions. The model is equivalent to a S = 1/2 XXZ model through a mapping S + i = b † i and S z i = n i − 1 2 [22,34]. Spin obeys commutation relations, [S α,i , S β,j ] = i ε αβγ S γ,i δ ij (5) where ε αβγ is the Levi-Civita symbol; α, β, γ ∈ (x, y, z) represent the spin direction; i, j are the sites on which the spins are located.…”

“…The superfluid density associated with a zigzag domain wall is much larger than that of an armchair domain wall due to the different arrangements of occupied and unoccupied sites along the domain wall. Recently, it is proposed that the zigzag domain wall can be created by nearest-neighbor repulsion in a self-organized way [22]. These results are also experimentally related to bosonic cold atoms trapped in optical lattices.…”