Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta = {1/2}$

TL;DR

This paper analytically solves the Bethe Ansatz equations for a finite XXZ spin chain with free boundaries and a complex surface field at the special anisotropy value , revealing the ground state structure.

Contribution

It provides an explicit analytic solution for the ground state of the finite XXZ spin chain at  anisotropy with specific boundary conditions and symmetry.

Findings

Derived the Bethe Ansatz solution for  anisotropy

Identified the ground state configuration for the finite chain

Connected the solution to the underlying quantum group symmetry

Abstract

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian. More precisely, we find one nontrivial solution, corresponding to the ground state of the system with anisotropy parameter $\Delta = {1/2}$ corresponding to $q^3 = -1$.