Title: Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems,
Abstract: 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. This generic proposal is illustrated
considering DQPTs occurring in the subsequent temporal evolution following a
sudden quench of the staggered mass of the topological Haldane model on a
hexagonal lattice where it stays fixed to zero or unity and makes a
discontinuous jump between these two values at critical times at which DQPTs
occur.