  We study the real-time dynamics of a small bubble of "false vacuum" in a
quantum spin chain near criticality, where the low-energy physics is described
by a relativistic (1+1)-dimensional quantum field theory. Such a bubble can be
thought of as a confined kink-antikink pair (a meson). We carefully construct
bubbles so that particle production does not occur until the walls collide. To
achieve this in the presence of strong correlations, we extend a Matrix Product
State (MPS) ansatz for quasiparticle wavepackets [Van Damme et al.,
arXiv:1907.02474 (2019)] to the case of confined, topological quasiparticles.
By choosing the wavepacket width and the bubble size appropriately, we avoid
strong lattice effects and observe relativistic kink-antikink collisions. We
use the MPS quasiparticle ansatz to detect scattering outcomes: In the Ising
model, with transverse and longitudinal fields, we do not observe particle
production despite nonintegrability (supporting recent observations of
nonthermalizing mesonic states). With additional interactions, we see
production of confined and unconfined particle pairs. Although we simulated
these low-energy, few-particle events with moderate resources, we observe
significant growth of entanglement with energy and with the number of
collisions, suggesting that increasing either will ultimately exhaust our
methods. Quantum devices, in contrast, are not limited by entanglement
production, and promise to allow us to go far beyond classical methods. We
anticipate that kink-antikink scattering in 1+1 dimensions will be an
instructive benchmark problem for relatively near-term quantum devices.
