Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1506.03964 · Physical Review A

Berry curvature of interacting bosons in a honeycomb lattice

Yun Li, Pinaki Sengupta, G. G. Batrouni, Christian Miniatura, Benoît Grémaud

Published Oct 6, 2015• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.92.043605

Related papers

Bosonic edge states in gapped honeycomb lattices

Huaiming Guo, Yuekun Niu, Shu Chen +1 more

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.

arXiv:1512.01340•Physical review. B./Physical review. B•Mar 1, 2016•9 citations

Hard-core bosonic domain walls on a honeycomb lattice

Xingchuan Zhu, Bo Li, Huaiming Guo +1 more

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.

arXiv:2005.07984•Physical Review A•Jun 5, 2020•3 citations

Quantum anomalous Hall states in the p -orbital honeycomb optical lattices

Machi Zhang, Hsiang-Hsuan Hung, Chuanwei Zhang +1 more

We study the quantum anomalous Hall states in the $p$-orbital bands of the honeycomb optical lattices loaded with single-component fermions. Such an effect has not yet been realized in both condensed-matter and cold-atom systems. By applying the available experimental techniques to rotate each lattice site around its own center, the band structures become topologically nontrivial. At a certain rotation angular velocity $\ensuremath{\Omega}$, a flat band structure appears with localized eigenstates carrying chiral current moments. By imposing the soft confining potential, the density profile exhibits a wedding-cake-shaped distribution with insulating plateaus at commensurate fillings. Moreover, the inhomogeneous confining potential induces dissipationless circulation currents, the magnitudes and chiralities of which vary with the distance from the trap center. In the insulating regions, the Hall conductances are quantized, and in the metallic regions, the directions and magnitudes of chiral currents can not be described by the usual local-density approximation. The quantum anomalous Hall effects are robust at temperature scales that are small compared to band gaps, which increase the feasibility of experimental realizations.

arXiv:1009.2133•Physical Review A•Feb 23, 2011•58 citations

Magnon edge states in the hardcore- Bose–Hubbard model

S. A. Owerre

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.

arXiv:1603.07989•Journal of Physics Condensed Matter•Sep 7, 2016•8 citations

A semiclassical study of the topological Bose-Hubbard model

S. A. Owerre

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-$1/2$ 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.

•Mar 25, 2016•0 citations

Phase diagram of interacting bosons on the honeycomb lattice

Stefan Weßel

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.

arXiv:cond-mat/0701337•Physical Review B•May 2, 2007•53 citations
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.
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.
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.
We study the quantum anomalous Hall states in the ppp-orbital bands of the honeycomb optical lattices loaded with single-component fermions. Such an effect has not yet been realized in both condensed-matter and cold-atom systems. By applying the available experimental techniques to rotate each lattice site around its own center, the band structures become topologically nontrivial. At a certain rotation angular velocity $\ensuremath{\Omega}$, a flat band structure appears with localized eigenstates carrying chiral current moments. By imposing the soft confining potential, the density profile exhibits a wedding-cake-shaped distribution with insulating plateaus at commensurate fillings. Moreover, the inhomogeneous confining potential induces dissipationless circulation currents, the magnitudes and chiralities of which vary with the distance from the trap center. In the insulating regions, the Hall conductances are quantized, and in the metallic regions, the directions and magnitudes of chiral currents can not be described by the usual local-density approximation. The quantum anomalous Hall effects are robust at temperature scales that are small compared to band gaps, which increase the feasibility of experimental realizations.
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.
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.