  We introduce and study dynamical probes of band structure topology in the
post-quench time-evolution from mixed initial states of quantum many-body
systems. Our construction generalizes the notion of dynamical quantum phase
transitions (DQPTs), a real-time counterpart of conventional equilibrium phase
transitions in quantum dynamics, to finite temperatures and generalized Gibbs
ensembles. The non-analytical signatures hallmarking these mixed state DQPTs
are found to be characterized by observable phase singularities manifesting in
the dynamical formation of vortex-antivortex pairs in the interferometric phase
of the density matrix. Studying quenches in Chern insulators, we find that
changes in the topological properties of the Hamiltonian can be identified in
this scenario, without ever preparing a topologically non-trivial or
low-temperature initial state. Our observations are of immediate relevance for
current experiments aimed at realizing topological phases in ultracold atomic
gases.
