光晶格中大自旋超冷费米原子的新奇量子相研究

The study of large-hyperfine-spin ultracold fermions has become a research focus at the interface of cold atom physics and condensed matter physics. High symmetries of SU(2N) and Sp(2N), which are difficult to realize in solids, naturally arise in large-hyperfine-spin ultracold fermion system. These symmetries not only give rise to even richer quantum phase structures than those in spin-1/2 systems, but also provide a unified view on competing orders in strongly correlated systems. We propose to investigate novel quantum phases of large-spin fermions in optical lattices, which are not accessible or stable in solids. The topics of interest include both the generic models of spin-3/2 fermions which are characterized by the Sp(4) symmetry, and the more special SU(2N) models which are valid for alkaline-earth fermions. The results can be straightforwardly generalized to the current experimental systems of Yb (2N=6) and Sr (2N=10). We plan to perform systematic nonperturbative determinant quantum Monte Carlo simulations on the novel SU(2N) and Sp(2N) magnetism, which are characterized by strong quantum fluctuations and competitions between antiferromagnetism and Cooper pairing. The proposed research will not only greatly deepen the understanding of quantum magnetism, but also provides theoretical support and guidance for experiments.

对光晶格中大超精细自旋超冷费米原子系统的研究目前已经成为冷原子物理和凝聚态物理交叉领域的热门研究方向。大自旋费米原子系统具有SU(2N)和Sp(2N)等在固体材料中难以实现的高对称性，高对称性不仅产生了比自旋1/2系统更加丰富的量子相结构，也提供了一个对量子强关联系统中竞争序的统一认识。我们提议在大自旋超冷费米原子系统中研究在通常固体材料中难以实现的新奇量子相，具体的课题包括一般的、具有Sp(4)对称性的自旋3/2费米子模型以及适用于碱土费米原子系统的SU(2N) Hubbard模型。这些结果可以直接推广到目前人们关注的冷原子实验系统，Yb（2N=6）和 Sr（2N=10）。SU(2N)和Sp(2N)量子磁性的特征是强量子涨落以及反铁磁和费米子配对的相互竞争。我们计划应用非微扰的行列式量子蒙特卡罗数值模拟方法，系统地研究这些新奇的量子磁性。此项研究将扩展我们对量子磁性的认识。

在光晶格中大自旋超冷费米原子体系中研究量子多体物理是凝聚态物理和冷原子物理交叉领域的重要前沿课题方向。在国家自然科学基金的资助下，我们采用大规模无符号问题的量子蒙特卡洛模拟方法，通过研究具有SU(N)对称性的半满格点Hubbard模型，来探索光晶格中大自旋超冷费米原子体系的量子磁性。我们研究了一系列与冷原子物理实验关注的体系直接相关的模型：六角蜂窝光晶格上的SU(4)和SU(6) Hubbard模型，具有PI磁通的正方光晶格上SU(4) Hubbard模型，一维光晶格上SU(N) Hubbard模型，具有交错构型磁通的正方光晶格上SU(4) Hubbard模型，六角蜂窝光晶格上SU(3)吸引Hubbard模型。通过对这些多自旋分量Hubbard模型的量子蒙特卡洛模拟研究，我们发现了一系列在大超精细自旋超冷费米原子体系中出现的、却在通常固体材料中难以实现的新奇量子相，并且利用数值方法研究了这些模型中量子相变的性质和临界行为。本项目的研究结果不仅拓展了对量子磁性的认识，而且为目前探索冷原子中新物质态的实验提供了理论支持。