Optimization of alloy-analogy-based approaches to the infinite-dimensional Hubbard model
Optimization of alloy-analogy-based approaches to the infinite-dimensional Hubbard model
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DOI：
10.1007/s100510050406
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发表时间：
1998-08
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影响因子：
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通讯作者：
M. Potthoff;T. Herrmann;W. Nolting
中科院分区：
文献类型：
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作者：
M. Potthoff;T. Herrmann;W. Nolting
提出了无限维Hubbard模型自能的解析表达式，该表达式在不同的精确可解极限之间插入。我们受益于基于合金类比（hubard - iii）解决方案的两种最新方法的结合：关注强耦合区域的修正合金类比（MAA）和正确恢复弱耦合区域的爱德华兹-赫兹方法（EHA）。研究EHA自身能量的高能量膨胀，结果发现EHA只复制了光谱密度的前三个确切已知时刻。这对于自磁学的研究可能是不够的。对CPA自洽方程的高能行为的分析允许对MAA的一种新的解释：MAA是唯一的（双组分）合金类比，它正确地考虑了谱密度的前四阶矩。然而，对于小u， MAA不能再现费米液体性质。新方法避免了MAA和EHA的缺陷。我们讨论了该理论的前景，并给出了与本质上精确的量子蒙特卡罗数据比较的数值结果。证明了自能的正确高能行为是可靠地描述自磁学的决定性因素。
An analytical expression for the self-energy of the infinite-dimensional Hubbard model is proposed that interpolates between different exactly solvable limits. We profit by the combination of two recent approaches that are based on the alloy-analogy (Hubbard-III) solution: the modified alloy-analogy (MAA) which focuses on the strong-coupling regime, and the Edwards-Hertz approach (EHA) which correctly recovers the weak-coupling regime. Investigating the high-energy expansion of the EHA self-energy, it turns out that the EHA reproduces the first three exactly known moments of the spectral density only. This may be insufficient for the investigation of spontaneous magnetism. The analysis of the high-energy behavior of the CPA self-consistency equation allows for a new interpretation of the MAA: the MAA is the only (two-component) alloy-analogy that correctly takes into account the first four moments of the spectral density. For smallU, however, the MAA does not reproduce Fermi-liquid properties. The defects of the MAA as well as of the EHA are avoided in the new approach. We discuss the prospects of the theory and present numerical results in comparison with essentially exact quantum Monte-Carlo data. The correct high-energy behavior of the self-energy is proved to be a decisive ingredient for a reliable description of spontaneous magnetism.