Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - 1/2 chain

verfasst von: Sascha Gehrmann, Gleb A. Kotousov, Sergei L. Lukyanov
Abstract: It is known that for the Heisenberg XXZ spin-\(\frac{1}{2}\) chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.
Organisationseinheit(en): Institut für Theoretische Physik
Externe Organisation(en): Rutgers University
Typ: Artikel
Journal: Nuclear Physics B
Band: 1006
Anzahl der Seiten: 47
ISSN: 0550-3213
Publikationsdatum: 09.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Kern- und Hochenergiephysik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2406.12102 (Zugang: Offen)
https://doi.org/10.1016/j.nuclphysb.2024.116624 (Zugang: Offen)

BibTeX

@article{5966fd0d556e470bbacc9ef5b3b2322f,
title = "Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - 1/2 chain",
abstract = "It is known that for the Heisenberg XXZ spin-\(\frac{1}{2}\) chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schr{\"o}dinger equation for the anharmonic oscillator. ",
author = "Sascha Gehrmann and Kotousov, {Gleb A.} and Lukyanov, {Sergei L.}",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",
year = "2024",
month = sep,
doi = "10.48550/arXiv.2406.12102",
language = "English",
volume = "1006",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier",
}