2017/06/30 by Takuya Kanazawa, Tilo Wettig · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Eigenvalues and eigenvectors #Fermion #Hamiltonian (control theory) #Mathematical physics #Matrix model #Operator (biology) #Physics #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Random matrix #Supersymmetry #Syk #cond-mat.str-el #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep09(2017)050
published as JHEP 09 (2017) 050 · 42 pages, 12 figures. v2: refs added
arxiv created 2017/08/30 · openalex publication_date 2017/09/01 · arxiv updated 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a complete symmetry classification of the Sachdev-Ye-Kitaev (SYK) model with N = 0, 1 and 2 supersymmetry (SUSY) on the basis of the Altland-Zirnbauer scheme in random matrix theory (RMT). For N = 0 and 1 we consider generic q-body interactions in the Hamiltonian and find RMT classes that were not present in earlier classifications of the same model with q = 4. We numerically establish quantitative agreement between the distributions of the smallest energy levels in the N = 1 SYK model and RMT. Furthermore, we delineate the distinctive structure of the N = 2 SYK model and provide its complete symmetry classification based on RMT for all eigenspaces of the fermion number operator. We corroborate our classification by detailed numerical comparisons with RMT and thus establish the presence of quantum chaotic dynamics in the N =2 SYK model. We also introduce a new SYK-like model without SUSY that exhibits hybrid properties of the N = 1 and N = 2 SYK models and uncover its rich structure both analytically and numerically.