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

Chinese Physics C

Mott-Hubbard transition of bosons in optical lattices with two-body interactions

燕花花, 马青山, Jun Zhang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In this paper, based on the Bose-Hubbard model with two-body on-site interactions, we study the quantum phase transition between the superfluid state and the Mott-insulator state. With the decoupling approximation, we get the relation between the weak superfluidity and dimensionless chemical potential with different particle number and different dimensionless interaction strength, and the relation between the weak superfluidity and the reciprocal of dimensionless interaction strength with different particle number. We also calculate the corresponding experimental parameters.更多还原

Related papers

Mott-Hubbard transition of bosons in optical lattices with two-body interactions

Hua-Hua Yan, Qing-Shan Ma, Jun Zhang

In this paper, based on the Bose-Hubbard model with two-body on-site interactions, we study the quantum phase transition between the superfluid state and the Mott-insulator state. With the decoupling approximation, we get the relation between the weak superfluidity and dimensionless chemical potential with different particle number and different dimensionless interaction strength, and the relation between the weak superfluidity and the reciprocal of dimensionless interaction strength with different particle number. We also calculate the corresponding experimental parameters.

Chinese Physics C•Jun 1, 2011•0 citations

Mott-Hubbard transition of bosons in optical lattices with three-body interactions

Bo-Lun Chen, Xiaobin Huang, Su-Peng Kou +1 more

In this paper, the quantum phase transition between the superfluid state and the Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating ``lobes'' and the existence of a fixed point in three-dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to observe our results through some experimental effects in optically trapped Bose-Einstein condensates is also discussed.

arXiv:0712.1696•Physical Review A•Oct 7, 2008•48 citations

Quantum phase transition of spin-2 cold bosons in an optical lattice

Jing-Min Hou, Mo‐Lin Ge

The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio ${c}_{0}/t$ ${(c}_{0}$ is the spin-independent on-site interaction and t is the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is a different phase boundary between superfluid and Mott-insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.

arXiv:cond-mat/0304428•Physical Review A•Jun 20, 2003•24 citations

Bose–Hubbard model with occupation-dependent parameters

Omjyoti Dutta, André Eckardt, Philipp Hauke +2 more

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.

arXiv:1009.1313•New Journal of Physics•Feb 9, 2011•59 citations

Superfluid-Mott-Insulator Phase Transition of Bosons in an Optical Lattice

Zhu Rui

The Bose–Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. We propose a mean-field theory based on a constraint SU(3) pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouin zone center, we find that the energy gaps vanish continuously around ( J XY / J z ) c ≈0.175 and ( J XY / J z ) c ≈0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mott insulator state changes into a superfluid state.

Communications in Theoretical Physics•May 1, 2007•1 citation

Quantum criticality of a Bose gas in an optical lattice near the Mott transition

Adam Rançon, N. Dupuis

We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass ${m}^{*}$ and scattering length ${a}^{*}$. Here ${m}^{*}$ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while ${a}^{*}$ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio $t/U$ between hopping amplitude and on-site repulsion.

arXiv:1107.1314•Physical Review A•Jan 4, 2012•13 citations
In this paper, based on the Bose-Hubbard model with two-body on-site interactions, we study the quantum phase transition between the superfluid state and the Mott-insulator state. With the decoupling approximation, we get the relation between the weak superfluidity and dimensionless chemical potential with different particle number and different dimensionless interaction strength, and the relation between the weak superfluidity and the reciprocal of dimensionless interaction strength with different particle number. We also calculate the corresponding experimental parameters.更多还原
In this paper, based on the Bose-Hubbard model with two-body on-site interactions, we study the quantum phase transition between the superfluid state and the Mott-insulator state. With the decoupling approximation, we get the relation between the weak superfluidity and dimensionless chemical potential with different particle number and different dimensionless interaction strength, and the relation between the weak superfluidity and the reciprocal of dimensionless interaction strength with different particle number. We also calculate the corresponding experimental parameters.
In this paper, the quantum phase transition between the superfluid state and the Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating ``lobes'' and the existence of a fixed point in three-dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to observe our results through some experimental effects in optically trapped Bose-Einstein condensates is also discussed.
The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio c0/t{c}_{0}/tc0​/t (c0{(c}_{0}(c0​ is the spin-independent on-site interaction and t is the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is a different phase boundary between superfluid and Mott-insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.
We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.
The Bose–Hubbard model describing interacting bosons in an optical lattice is reduced to a simple spin-1 XY model with single-ion anisotropy in the vicinity of the Mott phase. We propose a mean-field theory based on a constraint SU(3) pseudo-boson representation on the effective model to study the properties of the superfluid-Mott-insulator phase transition. By calculating the elementary excitation spectra and the average particle number fluctuation in the Brillouin zone center, we find that the energy gaps vanish continuously around ( J XY / J z ) c ≈0.175 and ( J XY / J z ) c ≈0.094 for 2D and 3D cubic lattices respectively, where the superfluid order parameters come up from zero and the Mott insulator state changes into a superfluid state.
We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure $P(\ensuremath{\mu},T)$ versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m∗{m}^{*}m∗ and scattering length a∗{a}^{*}a∗. Here m∗{m}^{*}m∗ is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while a∗{a}^{*}a∗ is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/Ut/Ut/U between hopping amplitude and on-site repulsion.