Quantum Quenches that Resemble Operator Growth

@misc{cao2026quantum,
  title = {{Quantum Quenches that Resemble Operator Growth}},
  author = {Xiangyu Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.23874},
  eprint = {2605.23874},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.23874},
}

TY  - UNPB
TI  - Quantum Quenches that Resemble Operator Growth
AU  - Xiangyu Cao
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2605.23874
UR  - https://arxiv.org/abs/2605.23874
AB  - 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 Lanzcos coefficients in generic quenches, a_m ∼ νm (diagonal), and b_m ∼ αm (off-diagonal), extending an operator growth hypothesis. We show that the growth quench dynamics is localized in both Krylov and Fock spaces when |ν| > 2 α, and derive a bound for the growth quench analogue of Lyapunov exponent λ_L ≤ √(4 α^2 − ν^2) when |ν| < 2 α. 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 grow 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 1D 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 suggest growth quenches as a promising approach to realize non-equilibrium coherent phenomena in many-body systems.
ER  -