2024/01/01 by Gehrmann, Sascha, Kotousov, Gleb A., Lukyanov, Sergei L.
Mathematics · Physics and Astronomy · #530 #Algebraic structures and combinatorial models #Anharmonic-Oscillators #Ansatz #Baxter #Conformal Field-Theory #High-Energy Qcd #Intergrable Structure #Invariance #Magnets #Q-Operators #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Staggered 6-Vertex Model
paper · doi:10.15488/20064
openalex publication_date 2024/01/01 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/01
It is known that for the Heisenberg XXZ spin - [Formula presented] 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.