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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.23874 |
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| _version_ | 1866917532864086016 |
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| author | Cao, Xiangyu |
| author_facet | Cao, Xiangyu |
| contents | 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, $a_m \sim νm$ (diagonal), and $b_m \sim αm$ (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 $λ_L \le \sqrt{4 α^2 - ν^2}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23874 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Quenches that Resemble Operator Growth Cao, Xiangyu Quantum Physics Statistical Mechanics 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, $a_m \sim νm$ (diagonal), and $b_m \sim αm$ (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 $λ_L \le \sqrt{4 α^2 - ν^2}$ 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. |
| title | Quantum Quenches that Resemble Operator Growth |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2605.23874 |