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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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.

Item Type:	Article
Uncontrolled Keywords:	Toeplitz Determinant ; Singularity
Subjects:	NATURAL SCIENCES > Physics > Condensed Matter Physics
Divisions:	Theoretical Physics Division
Projects:	Project title Project leader Project code Project type Novel Characterizations of Classical and Quantum Many-Body Systems-ManyBodyCharacteriza Fabio Franchini IP-2016-06-3347 HRZZ Frustrirani kompleksni sustavi-FCS Salvatore Marco Giampaolo IP-2019-04-3321 HRZZ
Depositing User:	Fabio Franchini
Date Deposited:	17 Feb 2021 08:08
URI:	http://fulir.irb.hr/id/eprint/6183
DOI:	10.1088/1751-8121/abcd55

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