截断Hilbert空间中强关联多粒子系统的模拟
Simulating strongly correlated multiparticle systems in a truncated Hilbert space
摘要：
用有限乘积基表示强相互作用的多粒子波函数会产生误差。简单的重新标度的接触相互作用可以保持低位的能量谱和长波长结构的波函数在一维系统，从而纠正基组截断误差。对于一个两粒子系统，当重标度是精确的时，得到了重标度的解析形式。有限Hilbert空间的计算结果和精确结果之间的详细比较多达5个粒子表明，重新标度可以显着提高各种外部势的数值计算的精度。除了基态能量外，还研究了低激发谱、密度分布和关联函数。这些结果为囚禁超冷原子的数值模拟提供了一个很好的前景。
英文摘要：
Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. Detailed comparison between finite Hilbert space calculations and exact results for up to 5 particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground state energies, the low-lying excitation spectrum, density profile and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.
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