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arXiv · 0910.0565

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

Vanja Dunjko·Maxim Olshanii
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Abstract

While Padé 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-Padé 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.

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Vanja Dunjko, Maxim Olshanii. 2009-10-03. A Hermite-Padé perspective on Gell-Mann--Low renormalization group: an application to the correlation function of Lieb-Liniger gas. https://arxiv.org/abs/0910.0565

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