Randomness and Chaos in Qubit Models

Abstract

We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$ SYK${}_2$ model at high temperatures that is absent in the $N=2$ SYK${}_2$ model. Our results suggest that this dip-ramp-plateau behavior implies the existence of random eigenvectors in a quantum many-body system. To further support this observation, we examine the Gaussian random transverse Ising model and obtain consistent results without suffering from small $N$ issues. Finally, we demonstrate numerically that expectation values of observables computed in a random quantum state at late times are equivalent to the expectation values computed in the thermal ensemble in a Gaussian random one-qubit model.

arXiv comment16 pages, 5 figures, minor changes, references added

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• Many-body level statistics of single-particle quantum chaos
• The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
• Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
• Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• What is the Simplest Linear Ramp?
• Quantum many-body dynamics on the star graph
• Correlated Disorder in the SYK${}_2$ model
• Spectral form factor in the double-scaled SYK model
• Spectral form factors of clean and random quantum Ising chains
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Towards the Web of Quantum Chaos Diagnostics
• Revealing nonperturbative effects in the SYK model
• Disorder-free Sachdev-Ye-Kitaev models: Integrability and a precursor of chaos
• Quantum Entanglement and Spectral Form Factor
• Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations
• Electronic properties of the boson mode in a three-point fermion loop and the emergent SYK physics
• Integrability and Spectral Form Factor in Chern-Simons Formulation