We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to 16 $\times$ 16 spins. In the ordered phase, the model exhibits dynamically constrained dynamics, leading to confinement of elementary excitations and slow thermalization. After demonstrating the signatures of confinement, we probe the dynamics of interfaces in the constrained regime through sudden quenches of product states with domains of opposite magnetization. We find that the nature of excitations can be captured by perturbation theory throughout the confining regime and identify the crossover to the deconfining regime. We systematically explore the effect of the transverse field on the modes propagating along flat interfaces and investigate the crossover from resonant to diffusive melting of a square of flipped spins embedded in a larger lattice.

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• Domain walls
• Ising model
• Perturbation theory
• Tensor network methods