Incremental expansions for the ground-state energy of the two-dimensional Hubbard model
Incremental expansions for the ground-state energy of the two-dimensional Hubbard model
复制标题
二维哈伯德模型基态能量的增量展开
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
K. Kladko
中科院分区：
文献类型：
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作者：
J. Málek;S. Flach;K. Kladko
Faddeev 的三体问题方法推广到多体问题导致了增量方法。该方法最近被应用于解释 HubbardPeiierls 链@J 的基态特性。 Malek、K. Kladko 和 S. Flach，JETP Lett。 67, 1052 ~1998!#.在这里，我们将这种方法推广到二维方格，并明确地将增量扩展处理到三阶。将我们的数值结果与各种其他方法进行比较〜蒙特卡罗，累积方法！我们证明增量扩展非常有效，因为这些方法仅处理由八个位点组成的晶格段即可实现良好的精度。 @S0163-1829~99!50408-6# 对强相互作用费米子性质的理解在过去十年中一直是研究的热门话题，部分原因是人们对高温超导体性质的兴趣。由于只有选定的可积模型才知道精确解，因此数值方法变得越来越重要，可以为必须使用各种近似值的分析方法提供基准。增量展开式已用于量子化学来解释分子和固体的性质。 1 在最近的一项工作 2 中，这些方法与累积量展开相结合，为数值实现提供了坚实的基础。结果之一是增量展开可以解释为求解多体问题的类法捷耶夫方程的近似方法。为了更详细地解释这一点，让我们考虑一个哈密顿量
A generalization of Faddeev’s approach of the three-body problem to the many-body problem leads to the method of increments. This method was recently applied to account for the ground-state properties of HubbardPeierls chains @J. Malek, K. Kladko, and S. Flach, JETP Lett. 67, 1052 ~1998!#. Here we generalize this approach to two-dimensional square lattices and explicitly treat the incremental expansion up to third order. Comparing our numerical results with various other approaches ~Monte Carlo, cumulant approaches! we show that incremental expansions are very efficient because good accuracy with these approaches is achieved treating lattice segments composed of eight sites only. @S0163-1829~99!50408-6# The understanding of properties of strongly interacting fermions has been an intense topic of research for the past decade, in part due to the interest in the properties of hightemperature superconductors. As exact solutions are known only for selected integrable models, numerical methods gained importance to provide benchmarks for analytical approaches that necessarily use approximations of all kinds. Incremental expansions have been used in quantum chemistry to account for properties of molecules and solids. 1 In a recent work 2 these methods were combined with cumulant expansions to provide a solid footing for numerical implementations. One result was that incremental expansions can be interpreted as approximative ways to solve Faddeev-like equations for the many-body problem. To explain this in more detail, let us consider a Hamiltonian