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:1211.6941 · New Journal of Physics

Quantum phases of hard-core bosons in a frustrated honeycomb lattice

Christopher N. Varney, Kai Sun, Victor M. Galitski, Marcos Rigol

Published Nov 28, 2012• 23 citations
arXivHTMLPDF

Abstract

Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose–Hubbard–Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.

DOI
10.1088/1367-2630/14/11/115028

Related papers

Phase diagrams of Bose-Hubbard model and antiferromagnetic spin-1/2 models on a honeycomb lattice

Takashi Nakafuji, Ikuo Ichinose

Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configuration of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte Carlo simulation. Besides the AF state, a ${120}^{\ensuremath{\circ}}$-order state, there appear other phases including a Bose metal in which no long-range orders exist.

arXiv:1705.06012•Physical Review A•Jul 26, 2017•11 citations

Extended Bose-Hubbard model on a honeycomb lattice

Jing Yu Gan, Yu Chuan Wen, Jinwu Ye +3 more

We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent $z=0.15$, which is smaller than results obtained on smaller lattices. This indicates that $z$ approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.

arXiv:cond-mat/0701120•Physical Review B•Jun 15, 2007•37 citations

Phase diagram of dipolar hard-core bosons on a honeycomb lattice

Takashi Nakafuji, Takeshi Ito, Yuya Nagamori +1 more

In this paper, we study phase diagrams of dipolar hard-core boson gases on a honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and nearest-neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte Carlo simulations, we investigate the system and show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found a coexisting phase of superfluid and chiral superfluid. Critical behaviors of the phase transitions are also clarified.

arXiv:1605.02492•Physical Review A•Aug 11, 2016•4 citations

Pair superfluid and supersolid of correlated hard-core bosons on a triangular lattice

Hong‐Chen Jiang, Liang Fu, Cenke Xu

We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.

arXiv:1204.3324•Physical Review B•Jul 24, 2012•21 citations

Polar molecules with three-body interactions on the honeycomb lattice

Lars Bonnes, Hans Peter Büchler, Stefan Weßel

We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in (Büchler et al 2007 Nat. Phys. 3 726), such a system is described by an extended Bose–Hubbard model of hard-core bosons that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground-state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime and determine the stability of the crystalline phases towards strong two-body interactions.

arXiv:0911.0312•New Journal of Physics•May 17, 2010•21 citations

Ground-state phase diagram of the two-dimensional extended Bose-Hubbard model

Takahiro Ohgoe, Takafumi Suzuki, Naoki Kawashima

We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.

arXiv:1206.3670•Physical Review B•Aug 27, 2012•55 citations
Using exact diagonalization calculations, we investigate the ground-state phase diagram of the hard-core Bose–Hubbard–Haldane model on the honeycomb lattice. This allows us to probe the stability of the Bose-metal phase proposed in Varney et al (2011 Phys. Rev. Lett. 107 077201), against various changes in the originally studied Hamiltonian.
Motivated by the recent experimental realization of the Haldane model by ultracold fermions in an optical lattice, we investigate phase diagrams of the hard-core Bose-Hubbard model on a honeycomb lattice. This model is closely related with a spin-1/2 antiferromagnetic (AF) quantum spin model. Nearest-neighbor (NN) hopping amplitude is positive and it prefers an AF configuration of phases of Bose-Einstein condensates. On the other hand, an amplitude of the next-NN hopping depends on an angle variable as in the Haldane model. Phase diagrams are obtained by means of an extended path-integral Monte Carlo simulation. Besides the AF state, a ${120}^{\ensuremath{\circ}}$-order state, there appear other phases including a Bose metal in which no long-range orders exist.
We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15z=0.15z=0.15, which is smaller than results obtained on smaller lattices. This indicates that zzz approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.
In this paper, we study phase diagrams of dipolar hard-core boson gases on a honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and nearest-neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte Carlo simulations, we investigate the system and show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found a coexisting phase of superfluid and chiral superfluid. Critical behaviors of the phase transitions are also clarified.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.
We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in (Büchler et al 2007 Nat. Phys. 3 726), such a system is described by an extended Bose–Hubbard model of hard-core bosons that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground-state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime and determine the stability of the crystalline phases towards strong two-body interactions.
We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.