标题： Gell-Mann--Low 重整化群的 Hermite-Padé 视角：Lieb-Liniger 气体相关函数的应用 显示英文标题

标题： A Hermite-Padé perspective on Gell-Mann--Low renormalization group: an application to the correlation function of Lieb-Liniger gas

摘要： 虽然有理逼近是一种改进级数展开收敛性的通用方法，但Gell-Mann--Low重正化群通常依赖于特殊对称性的存在。 我们表明，在单变量情况下，后者变为一个积分Hermite-Padé逼近，不需要特殊的对称性。 它特别适用于在变量小值的展开和大值的已知指数的标度定律之间进行插值。 作为一个例子，我们提取了Lieb-Liniger气体单体密度矩阵的标度定律前因子。 利用短距离展开中四阶项的新结果，我们发现与已知的第一性原理数值结果有显著的一致性。 显示英文摘要

摘要： While Pad\'e approximation is a general method for improving convergence of series expansions, Gell-Mann--Low renormalization group normally relies on the presence of special symmetries. We show that in the single-variable case, the latter becomes an integral Hermite-Pad\'e approximation, needing no special symmetries. It is especially useful for interpolating between expansions for small values of a variable and a scaling law of known exponent for large values. As an example, we extract the scaling-law prefactor for the one-body density matrix of the Lieb-Liniger gas. Using a new result for the 4th-order term in the short-distance expansion, we find a remarkable agreement with known ab initio numerical results.