Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox and establishing the unitarity of black hole evaporation. In this paper, we propose the dissipative Sachdev-Ye-Kitaev (SYK) model as a minimal quantum model that exhibits entanglement dynamics with features qualitatively similar to replica wormholes. As a demonstration, we investigate the entanglement growth of a pair of dissipative SYK models initialized in a thermofield double state. In the regime of large
N with weak dissipation, we observe a first-order entanglement transition characterized by a switch of the dominant saddle point: from replica-diagonal solutions for short times to replica wormholelike off-diagonal solutions for long times. Furthermore, we show that the signature of replica wormholes persists even at moderate $N\ensuremath{\lesssim}30$ by using the Monte Carlo quantum trajectory method. Our work may pave the way for explorations of replica wormhole physics in quantum simulators.
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.
The Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of fermions interacting with
q-body random couplings. For
q=2, it describes free particles and is nonchaotic in the many-body sense, while for
q>2 it is strongly interacting and exhibits many-body chaos. In this work we study the entanglement entropy (EE) of the
SYKq models for a bipartition of
N real or complex fermions into subsystems containing
2m real/
m complex fermions and $N\ensuremath{-}2m$/$N\ensuremath{-}m$ fermions in the remainder. For the free model
SYK2, we obtain an analytic expression for the EE, derived from the $\ensuremath{\beta}$-Jacobi random matrix ensemble. Furthermore, we use the replica trick and path-integral formalism to show that the EE is maximal when one subsystem is small, i.e., $m\ensuremath{\ll}N$, for arbitrary
q. We also demonstrate that the EE for the SYK4 model is noticeably smaller than the Page value when the two subsystems are comparable in size, i.e.,
m/N is
O(1). Finally, we explore the EE for a model with both SYK2 and SYK4 interactions and find a crossover from SYK2 (low-temperature) to SYK4 (high-temperature) behavior as we vary energy.
The Sachdev-Ye-Kitaev (SYK) model is a solvable model of a many-body quantum system that has stimulated interest in both condensed matter physics and quantum gravity. This review focuses on the insights provided by the SYK model, which has no quasiparticle excitations, into the physics of Planckian non-Fermi-liquid metals. This is discussed for a range of strongly correlated models and in relation to experiments on strongly correlated materials. Also included is a discussion of recent developments regarding the connections between the SYK model and the quantum theory of black holes.
Abstract Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-N limit. We find a first-order transition exist when tuning the subsystem size for the q = 4 case, while it is absent for the q = 2 case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly interacting SYK(-like) models.
Understanding the non-equilibrium dynamics of quantum many-body systems plays a central role in modern many-body physics. Intriguing insights emerge from investigating how quantum resources, which are essential for achieving unambiguous quantumness, are generated and spread under chaotic quantum dynamics. In fermionic systems, non-Gaussianity constitutes an important resource beyond entanglement, characterizing the deviation of generic quantum states from free-fermion states. In this Letter, we propose using the \textit{replica twist entropy}, defined through the expectation value of a replica rotation operator with a tunable angle
α, as a natural probe of non-Gaussianity in pure fermionic states. After deriving its behavior for typical many-body states, we establish a general framework for analyzing the replica twist entropy in solvable Sachdev-Ye-Kitaev models in the large-
N limit. Applying this framework to the dynamics of the thermofield double state, we uncover a novel dynamical phase diagram in the parameter space of
α and evolution time
t, exhibiting spontaneous
Z2 symmetry breaking at
α=π/4 and universal cusps as a function of
α in the long-time regime. Our results pave the way for studying non-Gaussianity in strongly correlated fermionic systems and reveal a new class of dynamical transitions probed by non-Gaussianity.