Home > Research > Publications & Outputs > Counting free fermions on a line

Research

Associated organisational units

Links

Text available via DOI:

Keywords

View graph of relations

Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit. / Ivanov, Dmitri A.; Abanov, Alexander G.; Cheianov, Vadim V.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 8, 085003, 01.03.2013.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ivanov, DA, Abanov, AG & Cheianov, VV 2013, 'Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit', Journal of Physics A: Mathematical and Theoretical, vol. 46, no. 8, 085003. https://doi.org/10.1088/1751-8113/46/8/085003

APA

Ivanov, D. A., Abanov, A. G., & Cheianov, V. V. (2013). Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit. Journal of Physics A: Mathematical and Theoretical, 46(8), Article 085003. https://doi.org/10.1088/1751-8113/46/8/085003

Vancouver

Ivanov DA, Abanov AG, Cheianov VV. Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit. Journal of Physics A: Mathematical and Theoretical. 2013 Mar 1;46(8):085003. doi: 10.1088/1751-8113/46/8/085003

Author

Ivanov, Dmitri A. ; Abanov, Alexander G. ; Cheianov, Vadim V. / Counting free fermions on a line : a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit. In: Journal of Physics A: Mathematical and Theoretical. 2013 ; Vol. 46, No. 8.

Bibtex

@article{e35a65d9ee9349df845f917be706e59d,
title = "Counting free fermions on a line: a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit",
abstract = "We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the 'counting parameter'. We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients.",
keywords = "MODEL, FIELD, EMPTINESS FORMATION PROBABILITY, XY SPIN CHAIN, FORMULAS, BOSE-GAS, PIECEWISE CONTINUOUS SYMBOLS, DISTANCE ASYMPTOTICS, TEMPERATURE",
author = "Ivanov, {Dmitri A.} and Abanov, {Alexander G.} and Cheianov, {Vadim V.}",
year = "2013",
month = mar,
day = "1",
doi = "10.1088/1751-8113/46/8/085003",
language = "English",
volume = "46",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "8",

}

RIS

TY - JOUR

T1 - Counting free fermions on a line

T2 - a Fisher-Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit

AU - Ivanov, Dmitri A.

AU - Abanov, Alexander G.

AU - Cheianov, Vadim V.

PY - 2013/3/1

Y1 - 2013/3/1

N2 - We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the 'counting parameter'. We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients.

AB - We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz and Wiener-Hopf determinants known as the generalized Fisher-Hartwig conjecture. The coefficients of this expansion are conjectured to obey certain periodicity relations, which renders the expansion explicitly periodic in the 'counting parameter'. We present two methods to calculate these coefficients and verify the periodicity relations order by order: the matrix Riemann-Hilbert problem and the Painleve V equation. We show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients.

KW - MODEL

KW - FIELD

KW - EMPTINESS FORMATION PROBABILITY

KW - XY SPIN CHAIN

KW - FORMULAS

KW - BOSE-GAS

KW - PIECEWISE CONTINUOUS SYMBOLS

KW - DISTANCE ASYMPTOTICS

KW - TEMPERATURE

U2 - 10.1088/1751-8113/46/8/085003

DO - 10.1088/1751-8113/46/8/085003

M3 - Journal article

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 8

M1 - 085003

ER -