Diffusion and operator entanglement spreading

Abstract

Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles. We derive the logarithmic bound $1/2\ln (t)$ for the $OSEE$ of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg $XXZ$ chain. Away from the isotropic point and from the free-fermion point, the $OSEE$ grows as $1/2\ln (t)$, irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent from probing the asymptotic behavior of the $OSEE$.

9 pages, 10 figures. Expanded version. As accepted in PRB

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Cited by in corpus (26)

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• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Scrambling is Necessary but Not Sufficient for Chaos
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Rule 54: Exactly solvable model of nonequilibrium statistical mechanics
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Entanglement Barriers in Dual-Unitary Circuits
• Temporal Entanglement in Chaotic Quantum Circuits
• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Entanglement entropy production in deep inelastic scattering
• Exact solution of the Floquet-PXP cellular automaton
• Magic Resources of the Heisenberg Picture
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• Boundary Chaos: Exact Entanglement Dynamics
• Bridging Entanglement and Magic Resources within Operator Space
• More on symmetry resolved operator entanglement
• Exact solution of the Rule 150 reversible cellular automaton
• Adversarial Robustness Guarantees for Quantum Classifiers
• Weighted Bures Length Uncovers Quantum State Sensitivity
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Random Permutation Circuits Beyond Qubits are Quantum Chaotic
• Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
• Krylov complexity of many-body localization: Operator localization in Krylov basis
• Volume-law entanglement entropy of typical pure quantum states