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arXiv:1603.07989 · Journal of Physics Condensed Matter

Magnon edge states in the hardcore- Bose–Hubbard model

S. A. Owerre

Published Sep 7, 2016• 8 citations
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Abstract

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.

DOI
10.1088/0953-8984/28/43/436003

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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 present a semiclassical perspective of the topological Bose-Hubbard model recently studied by quantum Monte Carlo (QMC) simulation on the honeycomb lattice [Phys. Rev. B 93, 121401(R) (2016)]. The three insulating phases uncovered by QMC are as follows: a superfluid, a Mott phase, and a charge-density-wave insulating phase. We show that this model maps to a spin-1/21/21/2 quantum XY model with competing magnetic fields on the two honeycomb sublattices. We give an explicit analytical origin of the quantum phase diagram using mean-field theory. Basically, the competition between the sublattice magnetic fields leads to three distinct phases uncovered by QMC. We find that the mean-field phase diagram captures a large regime of the quantum phase diagram. Furthermore, due to the mapping from bosons to spin variables and vice versa, the bosonic excitations of the Bose-Hubbard model correspond to the magnon excitations of the quantum spin system. We corroborate this assertion by computing the magnon bulk bands and the Berry curvatures and we find that the Berry curvatures have the same trends as the QMC result.
This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.
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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 $\ensuremath{\rho}=\frac{1}{2}$ 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.
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.
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.