Thermal Stability of Dynamical Phase Transitions in Higher Dimensional Stabilizer Codes

For all of the interest in dynamical phase transitions (DPT), it is still not clear the meaning or prevalence of these features in higher dimensional models. In this paper, we consider DPTs for stabilizer code models and quantum quenches between these models in higher dimensions, particularly $d=2,3$. We find that for many stabilizer codes, there exists a robust DPT to thermal noise which indicates the resilience of information stored in the ground space in the context of quantum error correction. That is, the critical temperature at which the DPT is lost corresponds to the theoretical upper-bound on the decoding rate for the code. We also discuss a generalization of the Wegner duality and how it can be used to characterize DPTs and other thermal properties.