能量最低的多体Fock态的有效构造
Efficient construction of many-body Fock states having the lowest energies
摘要：
为了在哈密顿量的精确对角化的框架下进行有效的多体计算，需要从单粒子轨道建立一个适当定制的Fock基。构成基的最简单的方法是选择一组有限的单粒子波函数，并找出这些状态中给定数量粒子的所有可能分布。然而，众所周知，这种结构导致非常不准确的结果，因为它没有考虑具有相同能量的不同多体状态。在这里，我们提出了一个快速和令人惊讶的简单的算法，用于生成多体Fock基础上建立从多体Fock状态具有最低的非相互作用的能量。该算法对单粒子能量分布的细节不敏感，并且可以用于服从玻色子或费米子统计的任意数量的粒子。此外，它可以很容易地推广到更大数量的组件。作为一个简单的例子，系统中的两个超冷玻色子在非谐陷阱，我们表明，精确计算的基础上产生的算法比标准的方法进行的计算更准确。
英文摘要：
To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states. It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing. Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis build from many-body Fock states having the lowest non-interacting energies. The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics. Moreover, it can be easily generalized to a larger number of components. Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.
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