  We study the Hall conductance of a Chern insulator after a global quench of
the Hamiltonian. The Hall conductance in the long time limit is obtained by
applying the linear response theory to the diagonal ensemble. It is expressed
as the integral of the Berry curvature weighted by the occupation number over
the Brillouin zone. We identify a topologically driven nonequilibrium phase
transition, which is indicated by the nonanalyticity of the Hall conductance as
a function of the energy gap m_f in the post-quench Hamiltonian H_f. The
topological invariant for the quenched state is the winding number of the
Green's function W, which equals the Chern number for the ground state of H_f.
In the limit that m_f goes to zero, the derivative of the Hall conductance with
respect to m_f is proportional to ln(|m_f|), with the constant of
proportionality being the ratio of the change of W at m_f = 0 to the energy gap
in the initial state. This nonanalytic behavior is universal in two-band Chern
insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb
model in the fermionic basis.
