String-Breaking Dynamics in Quantum Adiabatic and Diabatic Processes

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking: The separation of two charges results in an increase in the energy of a color flux, namely a string, connecting those charges. Eventually, creating additional dynamical charges is favored energetically, hence the string breaks. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatio-temporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for creating and analyzing string breaking in quantum-simulation experiments.