  We study the entanglement entropy scaling of the XXZ chain. While in the
critical XY phase of the XXZ chain the entanglement entropy scales
logarithmically with a coefficient that is determined by the associated
conformal field theory, at the ferromagnetic point, however, the system is not
conformally invariant yet the entanglement entropy still scales logarithmically
albeit with a different coefficient. We investigate how such an nontrivial
scaling at the ferromagnetic point influences the estimation of the central
charge $c$ in the critical XY phase. In particular we use the entanglement
scaling of the finite or infinite system, as well as the finite-size scaling of
the ground state energy to estimate the value of $c$. In addition, the
spin-wave velocity and the scaling dimension are also estimated. We show that
in all methods the evaluations are influenced by the nearby ferromagnetic point
and result in crossover behavior. Finally we discuss how to determine whether
the central charge estimation is strongly influenced by the crossover behavior
and how to properly evaluate the central charge.
