  We study the effects of electron correlations on the topological phase
transition in the Bernevig-Hughes-Zhang model using the variational cluster
approach where the short-range spatial correlations are taken into account
exactly. We calculate the spin Chern number and local magnetic moment to show
that the topologically nontrivial antiferromagnetic order exists and that the
magnetic transition is of the second order. We furthermore demonstrate that
under the spin-quantized condition the topological phase transition is caused
by the closing of the bulk band gap.
