Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos

• DOI: 10.48550/arxiv.2402.13154
• Publication Date: 2025-01-23
• Authors: Soshun Ozaki; Hosho Katsura
• Keywords: High Energy Physics - Theory; Condensed Matter - Strongly Correlated Electrons; Quantum Physics; Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Physics; QC1-999; FOS: Physical sciences; Quantum Physics (quant-ph); Condensed Matter - Statistical Mechanics

We introduce two disorder-free variants of the Sachdev-Ye-Kitaev (SYK) model, demonstrate their integrability, and study their static and dynamical properties. Unlike diagrammatic techniques, the integrability of these models allows us to obtain dynamical correlation functions even when the number of Majorana fermions is finite. From the solutions, we find that out-of-time-order correlators (OTOCs) in these models exhibit exponential growth at early times, resembling that of many-body quantum chaotic systems, such as those with disorder or external kick terms, despite their large N behavior differing from that of typical chaotic systems. Conversely, our analysis shows no evidence of random-matrix behavior in level spacing statistics or the spectral form factor. Our findings illustrate that the clean versions of the SYK models represent simple but nontrivial examples of disorder-free quantum many-body systems displaying chaoslike behavior of OTOCs. Published by the American Physical Society 2025