论文标题
通过相似性转化消除超低原子的波函数奇异性
Eliminating the wave function singularity for ultracold atoms by similarity transformation
论文作者
论文摘要
对于任何精确的数值模拟，$ s $ - 波相互作用原子的波功能中的双曲线奇异性是根问题。在这里，我们采用了相关的方法，从而通过两体jastrow因子明确描述了波功能的奇异性，然后通过相似性转换折叠到哈密顿量。由随机的Fock空间对角线化近似产生的非符号特征函数，其能量误差缩放为$ 1/m $的单粒子基函数的$ 1/m $。在与单一相互作用密切相关的费米子的示例中证明了超相关方法的性能。当前的方法在矩形盒中具有周期性边界条件的矩形盒子中提供了最准确的基态能量。
A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting non-singular eigenfunctions are approximated by stochastic Fock-space diagonalisation with energy errors scaling with $1/M$ in the number $M$ of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.
