When electron-electron correlations are important, it is often necessary touse exact numerical methods, such as Lanczos diagonalization, to study the fullmany-body Hamiltonian. Unfortunately, such exact diagonalization methods arerestricted to small system sizes. We show that if the Hubbard $U$ term isreplaced by a ``periodic Hubbard" term, the full many body Hamiltonian may benumerically exactly solved, even for very large systems (even $>$100 sites),though only for low fillings. However, for half-filled systems and large $U$this approach is not only no longer exact, it no longer improves extrapolationto larger systems. We discuss how generalized ``randomized variable averaging''(RVA) or ``phase randomization'' schemes can be reliably employed to improveextrapolation to large system sizes in this regime. This general approach canbe combined with any many-body method and is thus of broad interest andapplicability.
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机译：当电子-电子相关性很重要时，通常需要使用精确的数值方法（例如Lanczos对角化）来研究多体哈密顿量。不幸的是，这种精确的对角化方法仅限于较小的系统尺寸。我们显示，如果将“ Hubbard $ U $”项替换为““周期性Hubbard””项，则即使对于非常大的系统（甚至$> $ 100的站点），也可以用数字方式精确地求解整个哈密顿量，尽管这仅适用于低填充量。 ，对于半填充系统和大额美元，这种方法不仅不再精确，而且无法改善对大型系统的外推，我们将讨论广义的“随机变量平均”（RVA）或“阶段随机化”方案该方法可以与任何多体方法结合使用，因此具有广泛的兴趣和适用性。
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