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arXiv:2005.07984 · Physical Review A

Hard-core bosonic domain walls on a honeycomb lattice

Xingchuan Zhu, Bo Li, Huaiming Guo, Shiping Feng

Published Jun 5, 2020• 3 citations
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Abstract

Linelike hard-core bosonic domain walls in a staggered potential on a honeycomb lattice are studied using quantum Monte Carlo simulations. The phase diagrams of ribbons with zigzag and armchair domain walls are mapped, which contain superfluid and insulator phases at various fillings. In the $\ensuremath{\rho}=\frac{1}{2}$ insulator, the domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. 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. Our results provide a concrete context to study bosonic topological phenomena, which may be simulated experimentally using bosonic cold atoms trapped in optical lattices.

DOI
10.1103/physreva.101.063609

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Linelike hard-core bosonic domain walls in a staggered potential on a honeycomb lattice are studied using quantum Monte Carlo simulations. The phase diagrams of ribbons with zigzag and armchair domain walls are mapped, which contain superfluid and insulator phases at various fillings. In the \ensuremathρ=12\ensuremath{\rho}=\frac{1}{2}\ensuremathρ=21​ insulator, the domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. 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. Our results provide a concrete context to study bosonic topological phenomena, which may be simulated experimentally using bosonic cold atoms trapped in optical lattices.
For hardcore bosons on honeycomb lattice ribbons with zigzag edges, 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 $\ensuremath{\rho}=\frac{1}{2}$ filling. This self-organized domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall.
The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.
We study the phases of hard-core bosons on a two-dimensional periodic honeycomb lattice in the presence of an on-site potential with alternating sign along the different y-layers of the lattice. Using quantum Monte Carlo simulations supported by analytical calculations, we identify a weak topological insulator, characterized by a zero Chern number but non-zero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. Additionally, a charge-density-wave insulator is observed at 1/2-filling, whereas the phase diagram at intermediate densities is occupied by a superfluid phase. The weak topological insulator is further shown to be robust against any amount of nearest-neighbor repulsion, as well as weak next-nearest-neighbor repulsion. The experimental realization of our model is feasible in an optical lattice setup.
Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
We investigate the hardcore Bose-Hubbard model on a honeycomb lattice under a pseudo-magnetic field generated by triaxial strain using the quantum Monte Carlo (QMC) method. In the presence of strain, we construct a phase diagram that encompasses superfluid and solid phases at different fillings. Interestingly, we observe intriguing phenomena related to filling factors, including a solid phase with a filling of $\ensuremath{\rho}=0.4912$. This solid phase is characterized by distinct sublattice occupancies separated by large domain walls. Additionally, within the superfluid region, we observe stripe phases where the occupancy of hardcore bosons exhibits oscillatory behavior. Finally, we employ linear spin-wave theory and derive the pseudo-Landau levels present in the excitation spectrum. Our findings not only provide valuable insights into the behavior of hardcore bosons in the presence of pseudo-magnetic fields, but they can also be experimentally realized using ultracold bosonic atoms confined in optical lattices.