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:1007.0685 · Europhysics Letters (EPL)

Reference data for phase diagrams of triangular and hexagonal bosonic lattices

N. Teichmann, D. Hinrichs, Martin Holthaus

Published Jul 1, 2010• 24 citations
arXivHTMLPDF

Abstract

We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g -dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.

DOI
10.1209/0295-5075/91/10004

Related papers

Quantum phase transitions of ultracold Bose systems in nonrectangular optical lattices

Zhi Lin, Jun Zhang, Ying Yan Jiang

In this paper, we investigate systematically the Mott-insulator--superfluid quantum phase transitions for ultracold scalar bosons in triangular, hexagonal, and Kagom\'e optical lattices. With the help of the field-theoretical effective potential, by treating the hopping term in the Bose-Hubbard model as perturbation, we calculate the phase boundaries analytically for different integer filling factors. Our analytical results are in good agreement with recent numerical results.

arXiv:1112.4161•Physical Review A•Feb 14, 2012•11 citations

Process-chain approach to the Bose-Hubbard model: Ground-state properties and phase diagram

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus +1 more

We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made possible by a diagrammatic process-chain approach, derived from Kato's representation of the many-body perturbation series, which can be implemented numerically in a straightforward manner. We compute ground-state energies, atom-atom correlation functions, density-density correlations, and occupation number fluctuations, for one-, two-, and three-dimensional lattices with arbitrary integer filling. A phenomenological scaling behavior is found which renders the data almost independent of the filling factor. In addition, the process-chain approach is employed for calculating the boundary between the Mott insulator phase and the superfluid phase with high accuracy. We also consider systems with dimensionalities $d>3$, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.

arXiv:0904.0905•Physical Review B•Jun 12, 2009•57 citations

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

G. Mazzarella, S. M. Giampaolo, Fabrizio Illuminati

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.

arXiv:cond-mat/0509161•Physical Review A•Jan 26, 2006•76 citations

Phase diagram for ultracold bosons in optical lattices and superlattices

Pierfrancesco Buonsante, A. Vezzani

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.

arXiv:cond-mat/0405254•Physical Review A•Sep 22, 2004•88 citations

Process-chain approach and its application to bosonic lattice systems

Dennis Hinrichs, Niklas Teichmann, Martin Holthaus

We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for different lattice types. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor g and dimensionality d. Furthermore we clarify the g- and the d-dependence of the critical value and devise a method for extracting the critical value from the correlation function.

•Mar 12, 2010•0 citations

Bose-Hubbard phase diagram with arbitrary integer filling

Niklas Teichmann, Dennis Hinrichs, Martin Holthaus +1 more

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities $d>3$ and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.

arXiv:0810.0643•Physical Review B•Mar 6, 2009•65 citations
We investigate systems of bosonic particles at zero temperature in triangular and hexagonal optical lattice potentials in the framework of the Bose-Hubbard model. Employing the process-chain approach, we obtain accurate values for the boundaries between the Mott insulating phase and the superfluid phase. These results can serve as reference data for both other approximation schemes and upcoming experiments. Since arbitrary integer filling factors g are amenable to our technique, we are able to monitor the behavior of the critical hopping parameters with increasing filling. We also demonstrate that the g -dependence of these exact parameters is described almost perfectly by a scaling relation inferred from the mean-field approximation.
We carry out a perturbative analysis, of high order in the tunneling parameter, of the ground state of the homogeneous Bose-Hubbard model in the Mott insulator phase. This is made possible by a diagrammatic process-chain approach, derived from Kato's representation of the many-body perturbation series, which can be implemented numerically in a straightforward manner. We compute ground-state energies, atom-atom correlation functions, density-density correlations, and occupation number fluctuations, for one-, two-, and three-dimensional lattices with arbitrary integer filling. A phenomenological scaling behavior is found which renders the data almost independent of the filling factor. In addition, the process-chain approach is employed for calculating the boundary between the Mott insulator phase and the superfluid phase with high accuracy. We also consider systems with dimensionalities d>3d>3d>3, thus monitoring the approach to the mean-field limit. The versatility of the method suggests further applications to other systems which are less well understood.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such a result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.
We study the transition from a Mott insulator to a superfluid in the Bose-Hubbard model at zero temperature for different lattice types. Converting Kato's perturbation series into an efficient numerical algorithm capable of reaching high orders, we obtain accurate critical parameters for any filling factor g and dimensionality d. Furthermore we clarify the g- and the d-dependence of the critical value and devise a method for extracting the critical value from the correlation function.
We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities d>3d>3d>3 and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.