Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models

Abstract

We study operator dynamics in Brownian quantum many-body models with $q$-local interactions. The operator dynamics are characterized by the time-dependent size distribution, for which we derive an exact master equation in both the Brownian Majorana Sachdev-Ye-Kitaev (SYK) model and the spin model for general $q$. This equation can be solved numerically for large systems. Additionally, we obtain the analytical size distribution in the large $N$ limit for arbitrary initial conditions and $q$. The distributions for both models take the same form, related to the $\chi$-squared distribution by a change of variable, and strongly depend on the initial condition. For small initial sizes, the operator dynamics are characterized by a broad distribution that narrows as the initial size increases. When the initial operator size is below $q-2$ for the Majorana model or $q-1$ for the spin model, the distribution diverges in the small size limit at all times. The mean size of all operators, which can be directly measured by the out-of-time ordered correlator, grows exponentially during the early time. In the late time regime, the mean size for a single Majorana or Pauli operator for all $q$ decays exponentially as $t{e}^{-t}$, much slower than all other operators, which decay as $e^{-t}$. At finite $N$, the size distribution exhibits modulo-dependent branching within a symmetry sector for the $q\ge 8$ Majorana model and the $q\ge 4$ spin model. Our results reveal universal features of operator dynamics in $q$-local quantum many-body systems.

arXiv comment31 pages, 7 figures

References in corpus (38)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Comments on the Sachdev-Ye-Kitaev model
• Operator Spreading in Random Unitary Circuits
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Quantum Simulators: Architectures and Opportunities
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Random Quantum Circuits
• Towards the fast scrambling conjecture
• A Universal Operator Growth Hypothesis
• Verified Quantum Information Scrambling
• Information Scrambling in Computationally Complex Quantum Circuits
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Exact dynamics in dual-unitary quantum circuits
• Operator growth in the SYK model
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Symmetry enriched phases of quantum circuits
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Probing quantum information propagation with out-of-time-ordered correlators
• Locality, Quantum Fluctuations, and Scrambling
• Dynamics of quantum information
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Entanglement dynamics in quantum many-body systems
• Maximum velocity quantum circuits
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• Emergent perturbation independent decay of the Loschmidt echo in a many-spin system studied through scaled dipolar dynamics
• Operator Dynamics in Brownian Quantum Circuit
• Quantum chaos dynamics in long-range power law interaction systems
• Entanglement production and information scrambling in a noisy spin system
• Operator size at finite temperature and Planckian bounds on quantum dynamics
• Many-body quantum dynamics slows down at low density
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Note on entropy dynamics in the Brownian SYK model
• Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Complexity is not Enough for Randomness

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