Krylov complexity in the ergodically constrained nonintegrable transverse-field Ising model
Phys. Rev. B 113, 184207 – Published 11 May, 2026
DOI: https://doi.org/10.1103/45qp-ktk1
Abstract
The nonintegrable transverse-field Ising model is a common platform for studying ergodic quantum dynamics. In this work, we introduce a simple variant of the model in which this ergodic behavior is suppressed in the finite-size regime by introducing a spatial inhomogeneity in the interaction strengths. For this we partition the chain into two equal segments within which the spins interact with different coupling strengths. The ratio of these couplings defines an inhomogeneity parameter, whose variation away from unity leads to the mentioned constrained dynamics. We characterize this crossover using multiple diagnostics, such as the long-time saturation of out-of-time-ordered correlators, level-spacing statistics, and the spectral form factor. Making use of this tunable ergodic behavior, we can examine the impact of dynamical features towards operator spreading in the Krylov space and also for entanglement generation in the system's eigenstates. Unlike the monotonic behavior of the aforementioned diagnostics, the saturation of Krylov complexity shows a nontrivial suppression near the onset of constrained dynamics, which can be explained by quantifying the spread of the initial operator in the Krylov space. Together, these results demonstrate that introducing a macroscopic inhomogeneity in coupling strengths provides a minimal, disorder-free route to constraining the ergodic nature in this specific model of interacting spins, particularly in the finite-size regime. These effects are prominently reflected in a Krylov space analysis.
