Asymptotic behavior of Toeplitz determinants with a delta function singularity
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.
Keywords
Cite
@article{arxiv.2006.01922,
title = {Asymptotic behavior of Toeplitz determinants with a delta function singularity},
author = {Vanja Marić and Fabio Franchini},
journal= {arXiv preprint arXiv:2006.01922},
year = {2021}
}