Quenches, non-analyticities and emergent topology: Ising and Haldane models

Thermalization of a closed quantum system is a problem of immense interest.In this talk, we shall, however, focus on the early time dynamics of a closed quantum system evolving with the time independent final Hamiltonian following a quench. The purpose is to probe the emerging non-analyticities at different instants of time referred to as so called ``dynamical quantum phase transitions (DQPTs)''. These non-analyticties are manifested in the Loschmidt echo and can be connected to the the lines (or areas) of ``Fisher zeros'' in the complex time plane. Furthermore, these are reflected in a dynamical topological order parameter constructed out   of the gauge-independent Pancharatnam phase implying an emerging   topological structure. We shall illustrate the above scenario using the transverse Ising chain and topological Haldane model on a hexagonal lattice; for the latter model, we shall also illustrate the non-trivial role played by the Haldane mass term (which determines the topology of the equilibrium Haldane model).