标题： 一维成对跳跃和吸引 Hubbard 模型：比较研究 显示英文标题

标题： One-dimensional pair-hopping and attractive Hubbard models: A comparative study

摘要： 一维配对跳跃（PH）和吸引 Hubbard 模型的低能物理预期是相似的。 基于对小链的数值计算，几位作者最近对此观点提出了挑战，并预测在半填充和有限正耦合下，配对跳跃模型存在相变。 我们通过系统比较为 PH 模型和吸引 Hubbard 模型获得的数值结果，重新审视了这一争议。 为此，我们使用密度矩阵重整化群方法对大系统以及使用扭曲边界条件的 Lanczós 计算对小系统，计算了两个模型的 Luttinger 参数（自旋和电荷速度、刚度等）。 尽管我们的大多数结果确认了这两个模型非常相似，但我们发现之前数值研究中考虑的小尺寸（6-12 个站点）在自旋性质上存在一些重要差异。 然而，当我们考虑足够精确的本征态时，这些差异在较大尺寸（14-42 个站点）下消失了。 因此，我们的结果强烈表明，先前在小系统中发现的基态相变是一个有限尺寸的人工效应。 在 Luttinger 液体理论框架内解释我们的结果，我们讨论了微扰重整化群方法的预测与小尺寸数值计算之间明显矛盾的起源。 显示英文摘要

摘要： The low-energy physics of the one-dimensional Pair-Hopping (PH) and attractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenged this idea and predicted the existence of a phase transition at half-filling and finite positive coupling for the pair-hopping model. We re-examine the controversy by making systematic comparisons between numerical results obtained for the PH and attractive Hubbard models. To do so, we have calculated the Luttinger parameters (spin and charge velocities, stiffnesses, etc...) of the two models using both the Density Matrix Renormalization Group method for large systems and Lancz\'os calculations with twisted boundary conditions for smaller systems. Although most of our results confirm that both models are very similar we have found some important differences in the spin properties for the small sizes considered by previous numerical studies (6-12 sites). However, we show that these differences disappear at larger sizes (14-42 sites) when sufficiently accurate eigenstates are considered. Accordingly, our results strongly suggest that the ground-state phase transition previously found for small systems is a finite size artefact. Interpreting our results within the framework of the Luttinger liquid theory, we discuss the origin of the apparent contradiction between the predictions of the perturbative Renormalization group approach and numerical calculations at small sizes.