Thermal and dissipative effects on the heating transition in a driven critical system

We study the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system starting from pure initial states is well-described by Conformal Field Theory (CFT), which predicts existence both heating and non-heating phases such systems. Heating manifested via emergence black-hole like horizons system. robustness this CFT phenomenology when considering thermal open systems remains elusive. First, we present analytical results for Floquet time evolution states. Moreover, using exact calculations density matrix, demonstrate that short intermediate times, phase diagram comprising phases, persists on lattice. Secondly, fully with boundary dissipators, show nontrivial spatial structure survives particle-conserving non-conserving dissipations through clear signatures mutual information energy evolution.