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理论物理通讯：英文版

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

Zhu, Rui Rui

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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。

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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.

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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。
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.