Simulating strongly correlated multiparticle systems in a truncated Hilbert space
Simulating strongly correlated multiparticle systems in a truncated Hilbert space
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DOI：
10.1103/physreva.84.023623
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发表时间：
2011-04
影响因子：
2.9
通讯作者：
T. Ernst;D. Hallwood;J. Gulliksen;H. Meyer;J. Brand
中科院分区：
文献类型：
--
作者：
T. Ernst;D. Hallwood;J. Gulliksen;H. Meyer;J. Brand
在有限乘积基中表示强相互作用的多粒子波函数会导致误差。简单的重新标度的接触相互作用可以保持低的能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。最多五个粒子的有限希尔伯特空间计算和精确结果之间的详细比较表明，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，低的激发光谱，密度分布，和相关函数进行了研究。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。
Representing a strongly interacting multiparticle 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. A detailed comparison between finite Hilbert space calculations and exact results for up to five 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.