中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60512-060512.doi: 10.1088/1674-1056/ae48c6

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Thermodynamic and real-time dynamic properties of complex Sachdev-Ye-Kitaev model

Sizheng Cao(曹思政)1, Xian-Hui Ge(葛先辉)1,†, and Yi-Cheng Rui(芮易成)1,2,3   

  1. 1 Department of Physics, Shanghai University, Shanghai 200444, China;
    2 Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China;
    3 School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2026-01-08 修回日期:2026-02-18 接受日期:2026-02-23 发布日期:2026-06-05
  • 通讯作者: Xian-Hui Ge E-mail:gexh@shu.edu.cn
  • 基金资助:
    This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 12275166 and 12311540141).

Thermodynamic and real-time dynamic properties of complex Sachdev-Ye-Kitaev model

Sizheng Cao(曹思政)1, Xian-Hui Ge(葛先辉)1,†, and Yi-Cheng Rui(芮易成)1,2,3   

  1. 1 Department of Physics, Shanghai University, Shanghai 200444, China;
    2 Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China;
    3 School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2026-01-08 Revised:2026-02-18 Accepted:2026-02-23 Published:2026-06-05
  • Contact: Xian-Hui Ge E-mail:gexh@shu.edu.cn
  • Supported by:
    This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 12275166 and 12311540141).

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摘要： We study the complex Sachdev–Ye–Kitaev (cSYK) model numerically and investigate the thermodynamic behavior of the cSYK model across varying chemical potentials. We discover that the cSYK model remarkably mirrors the first-order phase transition seen in the van der Waals–Maxwell system, culminating at a non-mean-field critical point with distinctively different critical exponents. We analyze in detail the similarity between the van der Waals phase transition and the cSYK model, and further explore the mechanism by which the chemical potential drives the phase transition in the system. Exact diagonalization at finite N resolves the conserved U(1) charge sectors, showing that the chemical potential reshapes the density of states. Within each charge sector we find a strong level repulsion, while mixing sectors shows a Poisson distribution. The normalized spectral form factor displays a clear dip-ramp-plateau at low temperature for the neutral case, whereas for non-vanishing chemical potential the ramp is weakened by finite N reweighting of small edge sectors and only becomes visible at relatively high temperatures. Real-time dynamics, analyzed via analytical continuation of Schwinger–Dyson equations, show rapid decay in the gapless phase and prolonged oscillation lifetimes in the gapped regime. Spectral functions imply a shift from a continuous to a discrete energy level distribution, emphasizing the critical role of chemical potential in shaping spectral properties.

关键词: complex SYK model, van der Waals transition, spectral form factor, real-time dynamics

Abstract: We study the complex Sachdev–Ye–Kitaev (cSYK) model numerically and investigate the thermodynamic behavior of the cSYK model across varying chemical potentials. We discover that the cSYK model remarkably mirrors the first-order phase transition seen in the van der Waals–Maxwell system, culminating at a non-mean-field critical point with distinctively different critical exponents. We analyze in detail the similarity between the van der Waals phase transition and the cSYK model, and further explore the mechanism by which the chemical potential drives the phase transition in the system. Exact diagonalization at finite N resolves the conserved U(1) charge sectors, showing that the chemical potential reshapes the density of states. Within each charge sector we find a strong level repulsion, while mixing sectors shows a Poisson distribution. The normalized spectral form factor displays a clear dip-ramp-plateau at low temperature for the neutral case, whereas for non-vanishing chemical potential the ramp is weakened by finite N reweighting of small edge sectors and only becomes visible at relatively high temperatures. Real-time dynamics, analyzed via analytical continuation of Schwinger–Dyson equations, show rapid decay in the gapless phase and prolonged oscillation lifetimes in the gapped regime. Spectral functions imply a shift from a continuous to a discrete energy level distribution, emphasizing the critical role of chemical potential in shaping spectral properties.

Key words: complex SYK model, van der Waals transition, spectral form factor, real-time dynamics

中图分类号:  (Quantum statistical mechanics)

  • 05.30.-d
05.70.Fh (Phase transitions: general studies) 05.45.Mt (Quantum chaos; semiclassical methods)