Correlated disorder in the SYK₂ model

Abstract We study the SYK 2 model of N Majorana fermions with random quadratic interactions through a detailed spectral analysis and by coupling to two- four-point sources. In particular, we define generalized form factor (SFF) level spacing distribution function generalizing from partition generating function. For = 2, obtain an exact solution SFF. It exhibits qualitatively similar behavior higher case source term. The helps understand calculate mean value adjacent gap ratio defined term, find Gaussian unitary ensemble in near-integrable region theory, which indicates transition chaos. This is confirmed connected part SFF unfolded spectrum. departure this matrix as relative strength term increased consistent observation that alone, without couplings turned on, integrable spectrum large limit.