  The entanglement Chern number, the Chern number for the entanglement
Hamiltonian, is used to charac- terize the Kane-Mele model, which is a typical
model of the quantum spin Hall phase with the time reversal symmetry. We first
obtain the global phase diagram of the Kane-Mele model in terms of the
entanglement spin Chern number, which is defined by using a spin subspace as a
subspace to be traced out in preparing the entanglement Hamiltonian. We further
demonstrate the effectiveness of the entanglement Chern number without the time
reversal symmetry and spin conservation by extending the Kane-Mele model to
include the Zeeman term. The numerical results confirm that the sum of the
entanglement spin Chern number equals to the Chern number.
