Krylov complexity of a tilted extended Bose-Hubbard chain with Rydberg-dressed interactions
Abstract
We investigate Krylov state complexity in a tilted extended Bose-Hubbard chain in which both the on-site interaction U and nearest-neighbor interaction V are present. The tilted extended Bose-Hubbard model can be realized with Rydberg-dressed interactions in optical lattices. Using exact diagonalization and Lanczos recursion from three physically motivated Fock states, we compute the time-dependent complexity, its long-time saturation value, and the fluctuations of the Lanczos coefficients for an open chain at unit filling. Crucially, we identify a pronounced quasi-chaotic diagonal regime near U≃ V in which the Krylov complexity saturation exhibits a sharp ridge while the spectral level-spacing statistics remain partially chaotic. This dissociation arises from the competition between the on-site and nearest-neighbor interaction, which generates a dense manifold of near-resonant many-body configurations that is efficiently coupled by the state-dependent dynamics but retains residual spectral structure. Our results show that Krylov state complexity provides complementary, state-sensitive information about many-body chaos that is not captured by the spectral diagnostics alone, establishing Krylov complexity as a useful diagnostic for studying thermalization and information scrambling in experimentally accessible quantum simulators.
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BibTeX
@misc{chen2026krylov,
title = {{Krylov complexity of a tilted extended Bose-Hubbard chain with Rydberg-dressed interactions}},
author = {Yifan Chen and Tianyi Yan and Lu Qin and Weibin Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00712},
eprint = {2610.00712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00712},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Krylov complexity of a tilted extended Bose-Hubbard chain with Rydberg-dressed interactions
AU - Yifan Chen
AU - Tianyi Yan
AU - Lu Qin
AU - Weibin Li
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00712
UR - https://arxiv.org/abs/2610.00712
AB - We investigate Krylov state complexity in a tilted extended Bose-Hubbard chain in which both the on-site interaction U and nearest-neighbor interaction V are present. The tilted extended Bose-Hubbard model can be realized with Rydberg-dressed interactions in optical lattices. Using exact diagonalization and Lanczos recursion from three physically motivated Fock states, we compute the time-dependent complexity, its long-time saturation value, and the fluctuations of the Lanczos coefficients for an open chain at unit filling. Crucially, we identify a pronounced quasi-chaotic diagonal regime near U≃ V in which the Krylov complexity saturation exhibits a sharp ridge while the spectral level-spacing statistics remain partially chaotic. This dissociation arises from the competition between the on-site and nearest-neighbor interaction, which generates a dense manifold of near-resonant many-body configurations that is efficiently coupled by the state-dependent dynamics but retains residual spectral structure. Our results show that Krylov state complexity provides complementary, state-sensitive information about many-body chaos that is not captured by the spectral diagnostics alone, establishing Krylov complexity as a useful diagnostic for studying thermalization and information scrambling in experimentally accessible quantum simulators.
ER -