The Ising model has just turned 100 years, but it is still a source of interesting problems, especially out of equilibrium. In this talk, I consider its quantum version on the square lattice and discuss the evolution of coexisting ferromagnetic domains, which is relevant for understanding the quantum nucleation dynamics and the false-vacuum decay. I show that a smooth quantum-fluctuating interface delimiting a large two-dimensional domain can be studied in terms of a one-dimensional model via a "holographic" mapping when the Ising coupling is large. This model turns out to be an integrable chain of fermionic particles, the dynamics of which shows interesting connections with noteworthy results in mathematics as well as with similar problems in classical statistical physics. After discussing the interface dynamics on the lattice and in a suitable continuum limit, I provide evidence that the observed non-ergodic dynamics — due to the Stark localization of fermions — persists away from the infinite-Ising-coupling limit, and discuss some implications of our findings.