Nucleation of Sachdev-Ye-Kitaev Clusters in One Spatial Dimension
Abstract
We study how Sachdev-Ye-Kitaev (SYK) interactions can arise from localized single-particle states on a system that is effectively one dimensional. If a local interaction is projected onto coarse localized orbitals, the resulting couplings do not immediately follow the standard SYK distribution. Instead, they have a finite probability of being exactly zero, a broad non-Gaussian distribution for the nonzero values, and strong correlations coming from the geometry of the localized states. We then show that this changes when each localization volume is resolved into smaller microscopic pieces with random phases. As increases, the distribution of the nonzero couplings moves toward the complex-Gaussian SYK form. At the same time, the large- limit is a sparse but asymptotically canonical SYK network: the nonzero couplings create SYK clusters, while the pattern of missing or very weak couplings is still determined by the real-space overlap of the localized orbitals. Finally, we map the interaction tensor to a graph in pair space. This makes it possible to follow the formation, merger, and growth of SYK clusters, which we characterize using connected components and clique/simplex counts. The result is a minimal real-space phenomenological theory of SYK-cluster formation, providing clear experimental criteria.
Keywords
Cite
@article{arxiv.2604.08662,
title = {Nucleation of Sachdev-Ye-Kitaev Clusters in One Spatial Dimension},
author = {Hrant Topchyan and Tigran A. Sedrakyan},
journal= {arXiv preprint arXiv:2604.08662},
year = {2026}
}