A Riemann-Hilbert Approach to Slavnov Overlaps in the Lieb-Liniger model

Eldad Bettelheim

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arXiv · 2507.19025

A Riemann-Hilbert Approach to Slavnov Overlaps in the Lieb-Liniger model

Eldad Bettelheim

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Abstract

We provide a method to compute Slavnov overlaps in the Lieb-Liniger model using the steepest descent method of the Riemann-Hilbert problem. To do so, we employ the Matsuo-Kostov Representation of the Slavnov overlaps to write an integral equation for the respective resolvent, and then represent this equation as a Riemann-Hilbert problem. We demonstrate the validity and applicability of the method by computing the Anderson orthogonality catastrophe in the $c\to\infty$ limit, corresponding to free fermions.

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Eldad Bettelheim. 2025-07-25. A Riemann-Hilbert Approach to Slavnov Overlaps in the Lieb-Liniger model. https://arxiv.org/abs/2507.19025

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