Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-12 chain

authored by

Sascha Gehrmann, Gleb Andreevich 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.

Organisation(s)

Institute of Theoretical Physics

External Organisation(s)

Rutgers University

Type

Preprint

No. of pages

66

Publication date

2024

Publication status

E-pub ahead of print

Electronic version(s)

https://arxiv.org/abs/2406.12102 (Access: Open)