Local law and delocalization for the Sachdev-Ye-Kitaev model
Abstract
We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of N interacting Majorana fermions subject to a q-body interaction. For even q≪ N1/2, we prove that the normalized Stieltjes transform is approximated, uniformly on bounded energy intervals, by an explicit deterministic profile which we construct as an asymptotic expansion in the proportion αN,q of anticommuting q-body interaction terms. The result holds both on the full Hilbert space and in each fermion-parity sector. We derive mesoscopic eigenvalue counting and spectral form factor estimates. For fixed q, we further obtain high-probability ℓ∞-delocalization bounds in any deterministic orthonormal basis for individual bulk eigenvectors. These are the first mesoscopic laws and eigenvector delocalization estimates for the SYK Hamiltonian, which we obtain using the resolvent method.
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BibTeX
@misc{benigni2026local,
title = {{Local law and delocalization for the Sachdev-Ye-Kitaev model}},
author = {Lucas Benigni and Giorgio Cipolloni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.03771},
eprint = {2608.03771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03771},
}
RIS
TY - UNPB
TI - Local law and delocalization for the Sachdev-Ye-Kitaev model
AU - Lucas Benigni
AU - Giorgio Cipolloni
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.03771
UR - https://arxiv.org/abs/2608.03771
AB - We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of N interacting Majorana fermions subject to a q-body interaction. For even q≪ N^1/2, we prove that the normalized Stieltjes transform is approximated, uniformly on bounded energy intervals, by an explicit deterministic profile which we construct as an asymptotic expansion in the proportion α_N,q of anticommuting q-body interaction terms. The result holds both on the full Hilbert space and in each fermion-parity sector. We derive mesoscopic eigenvalue counting and spectral form factor estimates. For fixed q, we further obtain high-probability ℓ^∞-delocalization bounds in any deterministic orthonormal basis for individual bulk eigenvectors. These are the first mesoscopic laws and eigenvector delocalization estimates for the SYK Hamiltonian, which we obtain using the resolvent method.
ER -