Exact density matrix for quantum group invariant sector of XXZ model

Using the fermionic basis we obtain the expectation values of all $U_q(\text{slt})$-invariant local operators on 8 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. In the case when the $U_q(\text{slt})$ symmetry is not broken this computation is equivalent to finding the entire density matrix up to 8 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.