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

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 $\mathrm{\Delta }=1\mathrm{/}2$ corresponding to $q^3=-1$.