Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems

Understand

We introduce the notion of a dynamical topological order parameter (DTOP) that characterises dynamical quantum phase transitions (DQPTs) occurring in the subsequent temporal evolution of "two dimensional" closed quantum systems, following a quench (or ramping) of a parameter of the Hamiltonian, {which generalizes the notion of DTOP introduced in Budich and Heyl, Phys.

• Rev.
• B 93, 085416 (2016) for one-dimensional situations}.
• This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian.