Asymptotic behavior of Toeplitz determinants with a delta function singularity (CROSBI ID 290780)
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Podaci o odgovornosti
Marić, Vanja ; Franchini, Fabio
engleski
Asymptotic behavior of Toeplitz determinants with a delta function singularity
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.
Toeplitz Determinant ; Singularity
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Podaci o izdanju
54 (2)
2021.
025201
28
objavljeno
1751-8113
1751-8121
10.1088/1751-8121/abcd55