More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking

Abstract

We investigate the dynamics of the Rényi Operator Space Entanglement ($OSE$) entropies $S_n$ across several one-dimensional integrable and chaotic models. As a paradigmatic integrable system, we first consider the so-called rule $54$ chain. Our numerical results reveal that the Rényi $OSE$ entropies of diagonal operators with nonzero trace saturate at long times, in contrast with the behavior of von Neumann entropy. Oppositely, the Rényi entropies of traceless operators exhibit logarithmic growth with time, with the prefactor of this growth depending in a nontrivial manner on $n$. Notably, at long times, the complete operator entanglement spectrum ($ES$) of an operator can be reconstructed from the spectrum of its traceless part. We observe a similar pattern in the $XXZ$ chain, suggesting universal behavior. Additionally, we consider dynamics in nonintegrable deformations of the $XXZ$ chain. Finite-time corrections do not allow to access the long-time behavior of the von Neumann entropy. On the other hand, for $n>1$ the growth of the entropies is milder, and it is compatible with a sublinear growth, at least for operators associated with global conserved quantities. Finally, we show that in finite-size integrable systems, $S_n$ exhibit strong revivals, which are washed out when integrability is broken.

24 pages, 10 figures. Similar to published version

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement spectrum in one-dimensional systems
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Operator space entanglement entropy in transverse Ising chain
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Scrambling in Random Unitary Circuits: Exact Results
• Operator Space Entanglement Entropy in XY Spin Chains
• Scrambling is Necessary but Not Sufficient for Chaos
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Temporal Entanglement in Chaotic Quantum Circuits
• From Dual Unitarity to Generic Quantum Operator Spreading
• The entanglement membrane in exactly solvable lattice models

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