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

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 special symmetries. We show that in single-variable case, latter becomes an integral Hermite-Pad\'e approximation, needing no It especially useful interpolating between expansions small values variable and scaling law known exponent large values. As example, we extract scaling-law prefactor one-body density matrix Lieb-Liniger gas. Using new result 4th-order term short-distance expansion, find remarkable agreement with ab initio numerical results.