  We studied the entangled state for a one-dimensional $S=1/2$
antiferromagnetic quantum spin chain in a transverse field. We calculate the
ground state using the density matrix renormalization group and discuss how the
entangled state changes around a quantum phase transition (QPT) point. By
analyzing concurrence $C(\rho)$ for two-qubit density matrix $\rho$ after the
Lewenstein-Sanpera decomposition, $\rho=\Lambda \rho_s + (1-\Lambda) \rho_e $,
where $\rho_s$ is a separable density matrix and $\rho_e$ is a pure entangled
state obtained by a linear combination of Bell states, we find singular
behaviors both in $C(\rho_e)$ and $1-\Lambda$ at the QPT point.&#12288;
$C(\rho_e)$ includes the effects of quantum fluctuations, which manifest the
competition between the antiferromagnetic spin fluctuation and the effect of
transverse field in the transverse Ising model. The quantum fluctuation shows
the singular maximum at the QPT point as expected from the general picture of
phase transition. In contrast, $1-\Lambda$ reveals the singular minimum at QPT
point.
