Kibble-Zurek dynamics vs dissipation in critical spin chains

The dynamics of critical spin systems near quantum phase transitions are governed by universal behavior. Probing non-equilibrium criticality has been a major focus in ultra-cold physics, with dynamical protocols like the Kibble-Zurek mechanism and other quasi-adiabatic quenches emerging as invaluable techniques for many-body state preparation. However, in realistic experimental setups, decoherence and dissipation can significantly alter the expected universal behavior of the closed systems. While a few seminal studies have begun to address these discrepancies, the interplay between coherent and dissipative dynamics remain largely unexplored. We investigate these Kibble-Zurek driven-dissipative systems numerically (using MPS) and analytically (using fermionic techniques), beginning with the simplest integrable case, the quantum Ising model in 1+1 dimensions. The modified behavior of the correlations and entanglement are discussed in the case of both local and global dissipation channels.