Scaling limit of $Q$-functions for the ${\cal Z}_r$ invariant inhomogeneous XXZ spin-$\frac{1}{2}$ chain near free fermion point

TL;DR

This paper investigates the critical behavior of the ${ m Z}_r$ invariant inhomogeneous XXZ spin-1/2 chain near the free fermion point, deriving differential equations that describe the scaling limit of Bethe Ansatz solutions, linking integrable models and conformal symmetry.

Contribution

It introduces a class of differential equations capturing the scaling limit of Bethe Ansatz solutions for the ${ m Z}_r$ symmetric XXZ chain near the free fermion point, advancing the ODE/IQFT correspondence.

Findings

Derived differential equations for the scaling limit of Bethe solutions.

Linked the universal behavior to extended conformal symmetry.

Enhanced understanding of critical phenomena in integrable spin chains.

Abstract

At the beginning of the 70's, Baxter introduced a multiparametric generalization of the six-vertex model. This integrable system has been found to exhibit a remarkable variety of critical behaviors. The work is part of a series of papers devoted to their systematic study. We focus on the case when the lattice model possesses an additional ${\cal Z}_r$ symmetry and consider the critical behavior near the so-called free fermion point. Among other things, discussed is the algebra of extended conformal symmetry underlying the universal behavior. The main result of the paper is the class of differential equations that describe the scaling limit of the solutions to the Bethe Ansatz equations. This is an instance of the correspondence between Ordinary Differential Equations and Integrable Quantum Field Theory (ODE/IQFT correspondence).