Naslov
Asymptotic behavior of Toeplitz determinants with a delta function singularity

Autori
Marić, Vanja ; Franchini, Fabio

Izvornik
Journal of physics. A, Mathematical and theoretical (1751-8113) 54 (2021), 2; 025201, 28

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, ostalo

Ključne riječi
Toeplitz Determinant ; Singularity

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

POVEZANOST RADA