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arXiv · 2006.01922

Asymptotic behavior of Toeplitz determinants with a delta function singularity

Vanja Marić·Fabio Franchini
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Abstract

We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener-Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited states of some integrable models, where the delta function represents a peak at the momentum of the excitation. As a concrete example of applications of our results, using the derived asymptotic formulas we compute the spin-correlation functions in the lowest energy band of the frustrated quantum XY chain in zero field, and the ground state magnetization.

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Vanja Marić, Fabio Franchini. 2020-06-02. Asymptotic behavior of Toeplitz determinants with a delta function singularity. https://doi.org/10.1088/1751-8121%2Fabcd55

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