Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench

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