Correlation functions of the one-dimensional Hubbard model in a magnetic field

authored by: Holger Frahm, V. E. Korepin
Abstract: We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.
External Organisation(s): University of Virginia
Stony Brook University (SBU)
Type: Article
Journal: Physical Review B
Volume: 43
Pages: 5653-5662
No. of pages: 10
ISSN: 0163-1829
Publication date: 01.03.1991
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics
Electronic version(s): https://doi.org/10.1103/PhysRevB.43.5653 (Access: Unknown)
https://doi.org/10.15488/5091 (Access: Open)

BibTeX

@article{4f290b642cb8402580f32237985ce79c,
title = "Correlation functions of the one-dimensional Hubbard model in a magnetic field",
abstract = "We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.",
author = "Holger Frahm and Korepin, {V. E.}",
year = "1991",
month = mar,
day = "1",
doi = "10.1103/PhysRevB.43.5653",
language = "English",
volume = "43",
pages = "5653--5662",
journal = "Physical Review B",
issn = "0163-1829",
publisher = "American Institute of Physics",
number = "7",
}