  We propose characterization of the three-dimensional topological insulator by
using the Chern number for the entanglement Hamiltonian (entanglement Chern
number). Here we take the extensive spin partition of the system, that pulls
out the quantum entanglement between up spin and down spin of the many-body
ground state. In three dimensions, the topological insulator phase is described
by the section entanglement Chern number, which is the entanglement Chern
number for a periodic plane in the Brillouin zone. The section entanglement
Chern number serves as an interpolation of the $Z_2$ invariants defined on
time-reversal invariant planes. We find that the change of the section
entanglement Chern number protects the Weyl point of the entanglement
Hamiltonian and the parity of the number of Weyl points distinguishes the
strong topological insulator phase from the weak topological insulator phase.
