  We study the quantum relaxation of the two-dimensional transverse-field Ising
model after global quenches with a real-time variational Monte Carlo method and
address the question whether this non-integrable, two-dimensional system
thermalizes or not. We consider both interaction quenches in the paramagnetic
phase and field quenches in the ferromagnetic phase and compare the
time-averaged probability distributions of non-conserved quantities like
magnetization and correlation functions to the thermal distributions according
to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations
at temperatures defined by the excess energy in the system. We find that the
occurrence of thermalization crucially depends on the quench parameters: While
after the interaction quenches in the paramagnetic phase thermalization can be
observed, our results for the field quenches in the ferromagnetic phase show
clear deviations from the thermal system. These deviations increase with the
quench strength and become especially clear comparing the shape of the thermal
and the time-averaged distributions, the latter ones indicating that the system
does not completely lose the memory of its initial state even for strong
quenches. We discuss our results with respect to a recently formulated theorem
on generalized thermalization in quantum systems.
