Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model

Journal Article · Tue Nov 04 00:00:00 UTC 2025 · Physical Review. E

DOI: https://doi.org/10.1103/j589-dszc · OSTI ID:3021131

García-García, Antonio M. ^[1]; Liu, Chang  ^[2]; Sá, Lucas  ^[3]; Verbaarschot, Jacobus J. M.  ^[4]; Zheng, Jie-ping  ^[1]

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1. Shanghai Jiao Tong University (China)
2. Shanghai Qi Zhi Institute (China); Shanghai Jiao Tong University (China)
3. University of Cambridge (United Kingdom)
4. Stony Brook University, NY (United States)

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, 𝑁 Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For 𝑡≲√𝑁, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At 𝑡∼√𝑁, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading 1/𝑁 effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at 𝑡∼2⁢𝑁, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. Here, the oscillations at 𝑡≲√𝑁 indicate lack of thermalization—a desired feature for better performance of quantum information devices.

• Research Organization: Stony Brook University, NY (United States)
• Sponsoring Organization: National Natural Science Foundation of China (NSFC); USDOE
• Grant/Contract Number: FG02-88ER40388
• OSTI ID: 3021131
• Journal Information: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 5 Vol. 112; ISSN 2470-0053; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English