  Dynamical quantum phase transitions are at the forefront of current efforts
to understand quantum matter out of equilibrium. Except for a few exactly
solvable models, predictions of these critical phenomena typically rely on
advanced numerical methods. However, those approaches are mostly restricted to
one dimension, making investigations of two-dimensional systems highly
challenging. Here, we present evidence of dynamical quantum phase transitions
in strongly correlated spin lattices in two dimensions. To this end, we apply
our recently developed cumulant method [Phys. Rev. X 11, 041018 (2021)] to
determine the zeros of the Loschmidt amplitude in the complex plane of time and
predict the crossing points of the thermodynamic lines of zeros with the
real-time axis, where dynamical quantum phase transitions occur. We find the
critical times of a two-dimensional quantum Ising lattice and the XYZ model
with ferromagnetic or antiferromagnetic couplings. We also show how dynamical
quantum phase transitions can be predicted by measuring the initial energy
fluctuations, for example, in quantum simulators or other engineered quantum
systems.
