Emergent Dimensionality in Diluted Power-Law Quantum Walks
Abstract
We investigate single-excitation quantum walks across the one-to-two-dimensional crossover in diluted power-law hopping models. Using arrays of ℓ coupled chains of length L, we identify the finite-size localization crossover from the longitudinal spreading of an initially localized excitation. The crossover filling is well described by an exponential approach to its two-dimensional value with increasing ℓ, defining a characteristic transverse scale ℓe, and effectively two-dimensional behavior emerges already for ℓ≪ L. An independent spectral analysis shows that ℓe is set by the transverse extent of the eigenstates participating in the dynamics, providing a microscopic interpretation of the dimensional crossover. Our results reveal an intrinsic eigenstate scale governing emergent dimensionality in diluted systems with power-law hopping, a regime directly relevant to recently developed arrays of polar molecules, Rydberg atoms, and other quantum simulators with long-range interactions.
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BibTeX
@misc{dominguezcastro2026emergent,
title = {{Emergent Dimensionality in Diluted Power-Law Quantum Walks}},
author = {G. A. Domínguez-Castro and L. Santos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07856},
eprint = {2610.07856},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07856},
note = {CC0},
}
RIS
TY - UNPB
TI - Emergent Dimensionality in Diluted Power-Law Quantum Walks
AU - G. A. Domínguez-Castro
AU - L. Santos
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07856
UR - https://arxiv.org/abs/2610.07856
AB - We investigate single-excitation quantum walks across the one-to-two-dimensional crossover in diluted power-law hopping models. Using arrays of ℓ coupled chains of length L, we identify the finite-size localization crossover from the longitudinal spreading of an initially localized excitation. The crossover filling is well described by an exponential approach to its two-dimensional value with increasing ℓ, defining a characteristic transverse scale ℓ_e, and effectively two-dimensional behavior emerges already for ℓ≪ L. An independent spectral analysis shows that ℓ_e is set by the transverse extent of the eigenstates participating in the dynamics, providing a microscopic interpretation of the dimensional crossover. Our results reveal an intrinsic eigenstate scale governing emergent dimensionality in diluted systems with power-law hopping, a regime directly relevant to recently developed arrays of polar molecules, Rydberg atoms, and other quantum simulators with long-range interactions.
ER -