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Asymptotic behavior of Toeplitz determinants with a delta function singularity

Marić, Vanja; Franchini, Fabio (2021) Asymptotic behavior of Toeplitz determinants with a delta function singularity. Journal of Physics A: Mathematical and Theoretical, 54 (2). ISSN 1751-8113

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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.

Item Type: Article
Uncontrolled Keywords: Toeplitz Determinant ; Singularity
Subjects: NATURAL SCIENCES > Physics > Condensed Matter Physics
Divisions: Theoretical Physics Division
Project titleProject leaderProject codeProject type
Novel Characterizations of Classical and Quantum Many-Body Systems-ManyBodyCharacterizaFabio FranchiniIP-2016-06-3347HRZZ
Frustrirani kompleksni sustavi-FCSSalvatore Marco GiampaoloIP-2019-04-3321HRZZ
Depositing User: Fabio Franchini
Date Deposited: 17 Feb 2021 08:08
DOI: 10.1088/1751-8121/abcd55

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