Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at $\Delta$=1/2

We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at $\Delta=1/2$. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin-spin correlation functions, we have newly obtained the fourth- and fifth-neighbour transverse correlation functions. We have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. Using these results the exact values of the entanglement entropy for the reduced density matrix up six lattice sites have been obtained. We observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory.