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Logarithmic growth of operator entanglement in a clean nonintegrable circuit

Mao Tian Tan

Tomaž Prosen

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Phys. Rev. B 113, 224316 – Published 22 June, 2026

DOI: https://doi.org/10.1103/sqyj-5spd

Abstract

We study a so-called semiergodic brickwork dual-unitary circuit where, in the infinite volume limit, the two-point correlation functions of single-site operators exhibit ergodic behavior along one light ray and nonergodic behavior along the other light ray. Here, however, we study intermediate and long-time dynamics of a system in a finite, large volume. Under such dynamics, the Heisenberg evolution of a single traceless single-site operator lies within a restricted subspace, and this time evolution can be mapped to a simpler problem of a single qutrit scattering with a bunch of qubits sequentially. Despite the model being nonintegrable and free from any quenched disorder, the operator entanglement grows at most logarithmic in time, contrary to prior expectations. The autocorrelation function can be written in terms of a sum of products of SO(3) matrices, allowing for a random matrix prediction for the autocorrelation function at late times. The operator size distribution also becomes bimodal at certain times, displaying intermediate behavior between chaotic and free systems.

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Phys. Rev. B 113, 224316– Published 22 June, 2026
  • Received 1 April 2026
  • Accepted 14 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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