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arXiv:1512.01340 · Physical review. B./Physical review. B

Bosonic edge states in gapped honeycomb lattices

Huaiming Guo, Yuekun Niu, Shu Chen, Shiping Feng

Published Mar 1, 2016• 9 citations
arXivHTMLPDF

Abstract

By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we show the existence of bosonic edge states. For a single layer honeycomb lattice, bosonic edge states can be controlled to appear, cross the gap, and merge into bulk states by an on-site potential applied on the outermost sites of the boundary. On a bilayer honeycomb lattice, A bosonic edge state traversing the gap at half filling is demonstrated. The topological origin of the bosonic edge states is discussed with pseudo Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states with ultracold bosons trapped in honeycomb optical lattices.

DOI
10.1103/physrevb.93.121401

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By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we show the existence of bosonic edge states. For a single layer honeycomb lattice, bosonic edge states can be controlled to appear, cross the gap, and merge into bulk states by an on-site potential applied on the outermost sites of the boundary. On a bilayer honeycomb lattice, A bosonic edge state traversing the gap at half filling is demonstrated. The topological origin of the bosonic edge states is discussed with pseudo Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states with ultracold bosons trapped in honeycomb optical lattices.
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.
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.
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 consider soft-core bosons with on-site interaction loaded in the honeycomb lattice with different site energies for the two sublattices. Using both a mean-field approach and quantum Monte Carlo simulations, we show that the topology of the honeycomb lattice results in a nonvanishing Berry curvature for the band structure of the single-particle excitations of the system. This Berry curvature induces an anomalous Hall effect when driving the system out of equilibrium. It is seen by studying the time evolution of a wave packet, namely, a superfluid ground state in a harmonic trap, subjected either to a constant force (Bloch oscillations) or to a sudden shift of the trap center.
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
Conventional topological insulators exhibit exotic gapless edge or surface states, as a result of non-trivial bulk topological properties. In periodically-driven systems the bulk-boundary correspondence is fundamentally modified and knowledge about conventional bulk topological invariants is insufficient. While ultracold atoms provide excellent settings for clean realizations of Floquet protocols, the observation of real-space edge modes has so far remained elusive. Here we demonstrate an experimental protocol for realizing chiral edge modes in optical lattices, by creating a topological interface using a potential step that is generated with a programmable optical potential. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes that are realized in a periodically-driven honeycomb lattice. Controlling the height and sharpness of the potential step, we study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.