Spectral form factor of quadratic R-para-particle SYK model with Random Matrix Coupling

2025/04/27 by Tingfei Li, Li, Tingfei
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Random Matrices and Applications #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2504.19159

openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the spectral form factor (SFF) of the quadratic R-para-particle Sachdev-Ye-Kitaev (R-PSYK₂) model with various random matrix ensemble couplings. We generalize previous work on Gaussian Unitary Ensemble (GUE) couplings to all three Gaussian ensembles (GUE, GOE, GSE) and three circular ensembles (CUE, COE, CSE). Through analytical and numerical methods, we establish precise correspondences between GUE and CUE results, demonstrating their SFFs satisfy K_GUE(2t) ≈ K_CUE(t) in the time regime 1 ≪ t ≪ N. For the symplectic ensembles, we observe similar behavior with appropriate time rescaling, while we only provide the calculation method for the orthogonal ensembles.

Related

• Note on the q=2 R-para-fermionic SYK model
• Statistics of the Random Matrix Spectral Form Factor
• Derivation of the two Schwarzians effective action for the Sachdev-Ye-Kitaev spectral form factor
• The moments of the spectral form factor in SYK
• Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum