Logarithmic growth of operator entanglement in a clean non-integrable circuit

• URL: http://arxiv.org/abs/2603.19363v1
• Date: Thu, 19 Mar 2026 18:01:34 GMT
• Title: Logarithmic growth of operator entanglement in a clean non-integrable circuit
• Abstract summary: We study intermediate and long-time dynamics of a system in a finite, large volume.<n>Despite the model being non-integrable and free from any quenched disorder, the operator entanglement grows at most logarithmic in time.<n>The operator size distribution also becomes bimodal at certain times, displaying intermediate behavior between chaotic and free systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a so-called semi-ergodic brickwork dual-unitary circuits where, in the infinite volume limit, the two-point correlation functions of single-site operators exhibit ergodic behavior along one light ray and non-ergodic 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 non-integrable and free from any quenched disorder, the operator entanglement grows at most logarithmic in time, contrary to prior expectations. The auto-correlation function can be written in terms of a sum of products of $SO(3)$ matrices, allowing for a random matrix prediction for the auto-correlation 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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