Details
| Original language | English |
|---|---|
| Article number | 116624 |
| Number of pages | 47 |
| Journal | Nuclear Physics B |
| Volume | 1006 |
| Early online date | 11 Jul 2024 |
| Publication status | Published - Sept 2024 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Nuclear Physics B, Vol. 1006, 116624, 09.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - 1/2 chain
AU - Gehrmann, Sascha
AU - Kotousov, Gleb A.
AU - Lukyanov, Sergei L.
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85198988693&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2406.12102
DO - 10.48550/arXiv.2406.12102
M3 - Article
AN - SCOPUS:85198988693
VL - 1006
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
M1 - 116624
ER -