Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin $0\le S\le N/2$ in the neighborhood of the $\nu =1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical predictions for higher-order spatial and momentum correlations reveal intrinsic polygonal, multi-ring crystalline-type structures, which can be tested with ultracold-atom experiments in rapidly rotating traps, simulating quantum Hall physics (including quantum LLL skyrmions).

中文翻译：

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二维精确闭式解析波函数：快速旋转陷阱中接触相互作用的费米自旋超冷原子

任意数的精确二维解析波函数 $N$通过分析精确的哈密顿数值对角化数据，使用组合的数值和符号计算方法推导出接触相互作用的最低朗道能级 (LLL) 自旋费米子。给出了给定总角动量和总自旋下两类零相互作用能态的闭式解析表达式$0\le 秒\le N/2$ 在附近 $\nu =1$填充，覆盖从最大密度液滴到第一个准孔的范围。我们对高阶空间和动量相关性的理论预测揭示了内在的多边形、多环晶体型结构，可以在快速旋转陷阱中通过超冷原子实验进行测试，模拟量子霍尔物理学（包括量子 LLL 斯格明子）。