二维Hubbard反铁磁体的DMFT与二阶微扰理论
DMFT vs Second Order Perturbation Theory for the Trapped 2D Hubbard-Antiferromagnet
摘要：
在最近的超冷原子气体研究文献中，二维系统的计算通常是在动力学平均场论（DMFT）近似下进行的。在本文中，我们比较DMFT和一个完全二维的，自洽的二阶微扰理论的弱相互作用在排斥费米-哈伯德模型。我们调查的量子和空间波动的作用时，系统是在反铁磁相，并发现，虽然量子波动降低了序参量和临界温度急剧，空间波动只发挥显着的作用时，系统发生相变，或在相边界的陷阱。我们由此得出结论，DMFT是一个很好的近似的反铁磁费米-哈伯德模型的实验相关的系统尺寸。
英文摘要：
In recent literature on trapped ultracold atomic gases, calculations for 2D-systems are often done within the Dynamical Mean Field Theory (DMFT) approximation. In this paper, we compare DMFT to a fully two-dimensional, self-consistent second order perturbation theory for weak interactions in a repulsive Fermi-Hubbard model. We investigate the role of quantum and of spatial fluctuations when the system is in the antiferromagnetic phase, and find that, while quantum fluctuations decrease the order parameter and critical temperatures drastically, spatial fluctuations only play a noticeable role when the system undergoes a phase transition, or at phase boundaries in the trap. We conclude from this that DMFT is a good approximation for the antiferromagnetic Fermi-Hubbard model for experimentally relevant system sizes.
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