Green’s Function Approach to the Bose-Hubbard Model

• 作者: Axel Pelster Matthias Ohliger
• 来源期刊: 凝固态物理国际期刊(英文)
• 学科: 数学
• 关键词: Bose-Hubbard Model QUANTUM PHASE TRANSITION PHASE BOUNDARY
• 年，卷（期）: 2013,（2）
• 页码范围: 125-130
• 页数: 6页
• 分类号: O1

摘要

We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green’s function approach allows for calculating the excitation spectrum both for zero and finite temperature and for determining the effective masses of particles and holes.