We study growth quenches, which are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models, such as the East-West model. We point out a formal analogy with the dynamics of a local operator in the Heisenberg picture. Exploiting this analogy, we obtain several results on growth quenches by adapting operator-dynamics concepts and methods. First, applying the Krylov approach (recursion method), we conjecture the linear growth of Lanczos coefficients in generic quenches $a_m\sim \nu m$ (diagonal) and $b_m\sim \alpha m$ (off diagonal), extending an operator growth hypothesis. We show that the growth quench dynamics is localized in both Krylov and Fock spaces when $\left|\nu \right|>2\alpha$, and derive a bound for the growth quench analog of Lyapunov exponent ${\lambda }_L\le \sqrt{4{\alpha }^2-{\nu }^2}$ when $\left|\nu \right|<2\alpha$. Second, we realize the Fock localization in large-$N$ solvable growth quenches inspired by Sachdev-Ye-Kitaev (SYK) models. The bound on Lyapunov exponent is saturated in large-$q$ SYK growth quench. By contrast, the growth quench is almost always Fock localized in a nonrandom all-to-all growth quench amenable to semiclassics. Finally, in the one-dimensional East-West model, we interpret Fock-space cage states as the existence of a conserved charge. We show that the latter has ballistic transport due to current conservation. Moreover, adding hopping with a fine-tuned amplitude induces a partial localization due to a flat band. Our work suggests growth quenches as a promising approach to realize nonequilibrium coherent phenomena in many-body systems.

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• Ballistic transport
• Dynamical localization
• Quantum quench
• Sachdev-Ye-Kitaev model
• Semiclassical methods