Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

García-García, Antonio M.; Jia, Yiyang; Rosa, Dario; Verbaarschot, Jacobus J. M.

doi:10.1103/PhysRevD.103.106002

Title: Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

Journal Article · Mon May 03 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.103.106002· OSTI ID:1781178

García-García, Antonio M.;

; Rosa, Dario; Verbaarschot, Jacobus J. M.

We study a sparse Sachdev-Ye-Kitaev (SYK) model with N Majoranas where only ~ kN independent matrix elements are nonzero. We identify a minimum k ≳ 1 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 → 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 2^m-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.

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Research Organization:: State Univ. of New York (SUNY), Albany, NY (United States); Stony Brook Univ., NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC); Korea Institute of Advanced Study (KIAS)

Grant/Contract Number:: FAG-88FR40388; FG02-88ER40388; 11874259; PG059602

OSTI ID:: 1781178

Alternate ID(s):: OSTI ID: 1849986; OSTI ID: 2280817

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 103 Journal Issue: 10; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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