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arXiv 1105.1748cond-mat.quant-gas
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用量子蒙特卡罗方法研究幺正极限下的原子费米气体:相互作用范围的影响

Atomic Fermi gas at the unitary limit by quantum Monte Carlo methods: Effects of the interaction range

Xin Li, Jindrich Kolorenc, Lubos Mitas

摘要:

用扩散量子蒙特卡罗方法计算了非极化二组分费米气体的基态性质。通过外推到两粒子吸引相互作用的零有效射程,我们发现对于4、14、38和66个原子,$E/E_{\rm free}$分别为0.212(2)、0.407(2)、0.409(3)和0.398(3)。我们的结果表明,总能量对有效射程的依赖性很大,因此外推非常重要。为了测试节点表面的质量和估计的固定节点近似的影响,我们进行释放节点DMC计算4和14个原子。分析的释放节点和固定节点的结果表明,固定节点的错误的主要来源是长程相关性,这是很难在释放节点的方法,由于快速增长的玻色子噪声采样。除了能量,我们评估的两体密度矩阵和凝聚分数。我们发现,66原子系统的凝聚分数外推到零相互作用范围后收敛到0.56(1)。

英文摘要:

We calculate the ground-state properties of unpolarized two-component Fermi gas by the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find $E/E_{\rm free}$ to be 0.212(2), 0.407(2), 0.409(3) and 0.398(3) for 4, 14, 38 and 66 atoms, respectively. Our results indicate that the dependence of the total energy on the effective range is sizable and the extrapolation is therefore quite important. In order to test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66 atom system converges to 0.56(1) after the extrapolation to the zero interaction range.

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