Interface dynamics in the 2D quantum Ising model

In this talk, I will show how the dynamics of smooth interfaces in the 2D quantum Ising model can be addressed via a "holographic" mapping to a 1D integrable model of fermions, once the limit of large ferromagnetic coupling (J) is considered. I will discuss the localized dynamics emerging in this limit and how to account for corrections away from it, introducing a systematic 1/J expansion. I will also briefly discuss the scenario in presence of a random external field.