Understanding how quantum chaotic systems generate entanglement can provide insight into their microscopic chaotic dynamics and can help distinguish between different classes of chaotic behavior. Using von Neumann entanglement entropy, we study a nonentangled state evolved under three variants of the Sachdev-Ye-Kitaev (SYK) model with a finite number of Majorana fermions N. All the variants exhibit linear entanglement growth at early times, which at late times saturates to a universal value consistent with random matrix theory (RMT), but their growth rates differ. We interpret this as a large-N effect, arising from the enhanced nonlocality of fermionic operators in SYK and binary SYK, absent in spin operators of the spin-SYK model. Numerically, we find that these differences emerge gradually with increasing N. Although all variants are quantum chaotic, their entanglement dynamics reflect varying scrambling rates and indicate that the entanglement production rate serves as a fine-grained probe of scrambling beyond conventional measures. To probe its effect on the thermalization properties of these models, we study the two-point autocorrelation function, finding no differences between the SYK variants, but deviations from RMT predictions for N≥24, particularly near the crossover from exponential decay to saturation regime.
Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-
q model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.
Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large- N solvable models: the Sachdev—Ye—Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.
The complex Sachdev-Ye-Kitaev (SYK) model, featuring fermions with all-to-all interactions, serves as a dual paradigm for understanding non-Fermi liquid behavior and the holographic nature of charged black holes. Two defining characteristics of the standard SYK model are its maximal chaos (Lyapunov exponent
λL=2πT at temperature
T), and its finite zero-temperature residual entropy. While previous studies have largely focused on couplings drawn from a zero-mean Gaussian distribution, we investigate a generalized model with a finite mean-to-standard-deviation ratio,
g≡J0/δJ of the coupling distribution in order to get deeper insight into the evolution of chaos. We find that increasing
g yields the following effects: (i) The system remains a fast scrambler with
λL=A T, but with a suppressed coefficient
A<2π. (ii) In the limit
g→∞, out-of-time-ordered correlators (OTOCs) no longer exhibit exponential growth with
λL≃0. (iii) The spectral correlations indicative of late-time chaos maintain Wigner-Dyson level spacing statistics for all values of
g. (iv) The system preserves a finite residual entropy, albeit with reduced magnitude, for all
g values. We conclude that in this generalized SYK model, there is a chaotic to non-chaotic crossover. Moreover different measures of chaos decouple, demonstrating that the presence of finite residual entropy does not strictly imply maximal chaos.
Recent investigations of Rényi entanglement entropy in the Sachdev-Ye-Kitaev (SYK) chain of Majorana fermions have indicated that the model exhibits slow thermalization when initialized in certain states. The extent to which the heavy modes—believed to underlie this behavior—affect other aspects of the model remains an open question. In this work, I study thermalization and scrambling of information in individual energy eigenstates of the SYK chain using exact diagonalization. I show that two-point correlation functions in finite-energy eigenstates closely match their thermal counterparts and that information scrambling occurs efficiently within these pure states. These results suggest that the slow thermalization observed in entanglement dynamics does not extend to all probes of thermalization and scrambling, even in pure states.
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.
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≲sqrt[N], after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At t∼sqrt[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∼2N, 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. The oscillations at t≲sqrt[N] indicate lack of thermalization-a desired feature for better performance of quantum information devices.