  We study holographic entanglement entropy in 5-dimensional charged black
brane geometry obtained from Einstein-SU(2)Yang-Mills theory defined in
asymptotically AdS space. This gravity system undergoes second order phase
transition near its critical point affected by a spatial component of the
Yang-Mills fields, which is normalizable mode of the solution. This is known as
phase transition between isotropic and anisotropic phases. We get analytic
solutions of holographic entanglement entropies by utilizing the solution of
bulk spacetime geometry given in arXiv:1109.4592, where we consider subsystems
defined on AdS boundary of which shapes are wide and thin slabs and a cylinder.
It turns out that the entanglement entropies near the critical point shows
scaling behavior such that for both of the slabs and cylinder,
$\Delta_\varepsilon S\sim\left(1-\frac{T}{T_c}\right)^\beta$ and the critical
exponent $\beta=1$, where $\Delta_\varepsilon S\equiv S^{iso}-S^{aniso}$, and
$S^{iso}$ denotes the entanglement entropy in isotropic phase whereas
$S^{aniso}$ denotes that in anisotropic phase. We suggest a quantity
$O_{12}\equiv S_1-S_2$ as a new order parameter near the critical point, where
$S_1$ is entanglement entropy when the slab is perpendicular to the direction
of the vector order whereas $S_2$ is that when the slab is parallel to the
vector order. $O_{12}=0$ in isotropic phase but in anisotropic phase, the order
parameter becomes non-zero showing the same scaling behavior. Finally, we show
that even near the critical point, the first law of entanglement entropy is
hold. Especially, we find that the entanglement temperature for the cylinder is
$\mathcal T_{cy}=\frac{c_{ent}}{a}$, where $c_{ent}=0.163004\pm0.000001$ and
$a$ is the radius of the cylinder.
