  We study the dynamical process of equilibration of topological properties in
quantum many-body systems undergoing a parameter quench between two
topologically inequivalent Hamiltonians. This scenario is motivated by recent
experiments on ultracold atomic gases, where a trivial initial state is
prepared before the Hamiltonian is ramped into a topological insulator phase.
While the many-body wave function must stay topologically trivial in the
coherent post-quench dynamics, here we show how the topological properties of
the single particle density matrix dynamically change and equilibrate in the
presence of interactions. In this process, the single particle density matrix
goes through a characteristic level crossing as a function of time, which plays
an analogous role to the gap closing of a Hamiltonian in an equilibrium
topological quantum phase transition. As an exact case study exemplifying this
mechanism, we numerically solve the quench dynamics of an interacting
one-dimensional topological insulator.
