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Communications in Theoretical Physics

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

Zhu Rui

Published May 1, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0253-6102/47/5/026

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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.
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. In the strong coupling Mott insulating regime, we propose a mean field theory based on a constraint SU (3) pseudo-boson representation on the effective model and discuss the excitation spectra and the phase transition to the superfluid state. Further to the superfluid phase, we use the coherent-state approach to derive the collective excitation modes. It is found that the Mott phase has two degenerate gapped quadratic excitation spectra which graduate into two degenerate gapless linear ones at the transition point, and one gapless linear mode with one gapped quadratic mode in the superfluid phase.
在一个光格子描述交往的波色子的 Bose-Hubbard 模型在大草原上的树丛阶段的附近与单个离子的 anisotropy 被归结为一个简单 spin-1 XY 模型。我们在有效模型上基于一个限制苏(3 ) 伪波色子代表建议一个吝啬地的理论学习 superfluid-Mott-insulator 阶段转变的性质。在 theBrillouin 地区的基本刺激系列和平均粒子数字变化集中的 Bycalculating ，我们发现精力差距连续地消失在附近(J_( XY ) /J_z ) _c ≈0 .175 并且(J_( XY ) /J_z ) _c ≈ 0.094 为 2D 和 3D 立方的格子分别地，在超流体顺序参数从零来，进超流体的莫特绝缘体状态变化说的地方。
We study the superfluid--Mott insulator (SF-MI) transition of spin-1 bosons interacting antiferromagnetically in an optical lattice. Starting from a Bose-Hubbard tight-binding model for spin-1 bosons, we obtain the zero-temperature phase diagram by a mean-field approximation. We find that the MI phase with an even number of atoms per site is a spin singlet state, while the MI phase with an odd number of atoms per site has spin 1 at each site in the limit of t=0t=0t=0, where ttt is the hopping matrix element. We also show that the superfluid phase is a polar state as in the case for a spin-1 Bose condensate in a harmonic trap. It is found that the MI phase is strongly stabilized against the SF-MI transition when the number of atoms per site is even, due to the formation of singlet pairs. We derive the effective spin Hamiltonian for the MI phase with one atom per site and briefly discuss the spin order in the MI phase.
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the chemical potential. We calculate the excitation spectra as a useful probe to identify the quantum phases and the SF-to-MI transitions. In the excitation spectra of the SF phase, there are two gapless modes and a few gapful modes, which respectively correspond to phase and amplitude fluctuations of the order parameters. At the SF-to-MI transition point, we show that the energy gaps of certain amplitude modes reach zero for the second-order transition while they remain finite for the first-order one. Since the excitation spectrum can be measured by the Bragg scattering, we calculate the dynamical structure factor by using the linear response theory. We consider three types of density fluctuations, and show that the density fluctuations are coupled to different excitation branches in different quantum phases.
We analyze theoretically the emergence of different superfluid phases of spin-1 bosons in a three-dimensional cubic optical lattice by generalizing the recently developed Ginzburg–Landau theory for the Bose–Hubbard model to a spinor Bose gas. In particular at zero temperature, our theory distinguishes within its validity range between various superfluid phases for an anti-ferromagnetic interaction with an external magnetic field. In addition, we determine that the superfluid–Mott insulator phase transition is of second order and that the transitions between the respective superfluid phases with anti-ferromagnetic interaction can be both of first and second order.
We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.