(Non-)Thermalization in the 2D transverse field Ising model after quantum quenches

We study the quantum relaxation of the two-dimensional transverse field Ising model after a sudden quench with time-dependent variational Monte Carlo and focus on the question whether this non-integrable, two-dimensional system thermalizes or not. The time-averaged probability distribution of non-conserved quantities like magnetization and correlation functions is computed and compared with the thermal (canonical) distributions obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy after the quench. We find a good agreement of time-averaged and thermal distributions for small quenches far away from the critical point and a continuously increasing discrepancy between the two distributions for increasing quench strengths closer to the critical point. The shape of the time-averaged distributions indicates that the system does not completely lose its memory of the initial state even for strong quenches during the quantum relaxation process.