2020/07/27 by Antonio M. García-García, Antonio M. Garcı́a-Garcı́a, Yiyang Jia +3 · 73 citations
Mathematics · Physics and Astronomy · #Combinatorics #Degenerate energy levels #Dual polyhedron #Eigenvalues and eigenvectors #Fibonacci number #Mathematical physics #Mathematics #Physics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum gravity #Quantum many-body systems #Quantum mechanics #Random matrix #Scaling #Statistical physics #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · open access · doi:10.1103/physrevd.103.106002
published in Physical review. D/Physical review. D. 103(10) (American Physical Society) · 48 pages, 26 figures
arxiv created 2020/07/27 · openalex created_date 2020/08/03 · openalex publication_date 2021/05/03 · arxiv updated 2021/05/12 · openalex updated_date 2026/08/05
We study a sparse Sachdev-Ye-Kitaev (SYK) model with N Majoranas where only \ensuremath∼kN independent matrix elements are nonzero. We identify a minimum k\ensuremath\gtrsim1 for quantum chaos to occur by a level statistics analysis. The spectral density in this region, and for a larger k, is still given by the Schwarzian prediction of the dense SYK model, though with renormalized parameters. Similar results are obtained for a beyond linear scaling with N of the number of nonzero matrix elements. This is a strong indication that this is the minimum connectivity for the sparse SYK model to still have a quantum gravity dual. We also find an intriguing exact relation between the leading correction to moments of the spectral density due to sparsity and the leading 1/d correction of Parisi's U(1) lattice gauge theory in a d-dimensional hypercube. In the k\ensuremath→1 limit, different disorder realizations of the sparse SYK model show emergent random matrix statistics that for fixed N can be in any universality class of the tenfold way. The agreement with random matrix statistics is restricted to short-range correlations, no more than a few level spacings, in particular in the tail of the spectrum. In addition, emergent discrete global symmetries in most of the disorder realizations for k slightly below one give rise to 2m-fold degenerate spectra, with m being a positive integer. For k=3/4, we observe a large number of such emergent global symmetries with a maximum 28-fold degenerate spectra for N=26.