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Square-root growth of operator entanglement in an integrable brickwork circuit
Abstract
It is widely expected that the von Neumann entanglement of a local operator grows at most logarithmically in integrable many-body systems in infinite volume. We give a counterexample in a four-state brickwork circuit whose gate is a permutation matrix solving the constant Yang--Baxter equation. The von Neumann operator entropy grows as (log2)√(t/π)+O(log t), whereas fixed-index Rényi entropies grow linearly below index one and logarithmically above it. At fixed relative Hilbert--Schmidt error below one, matrix product operator simulations require a bond dimension growing at least as exp(c√t) for some c>0.
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BibTeX
@misc{pozsgay2026squareroot,
title = {{Square-root growth of operator entanglement in an integrable brickwork circuit}},
author = {Balázs Pozsgay},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39401},
eprint = {2609.39401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39401},
}
RIS
TY - UNPB
TI - Square-root growth of operator entanglement in an integrable brickwork circuit
AU - Balázs Pozsgay
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.39401
UR - https://arxiv.org/abs/2609.39401
AB - It is widely expected that the von Neumann entanglement of a local operator grows at most logarithmically in integrable many-body systems in infinite volume. We give a counterexample in a four-state brickwork circuit whose gate is a permutation matrix solving the constant Yang--Baxter equation. The von Neumann operator entropy grows as (log2)√(t/π)+O(log t), whereas fixed-index Rényi entropies grow linearly below index one and logarithmically above it. At fixed relative Hilbert--Schmidt error below one, matrix product operator simulations require a bond dimension growing at least as exp(c√t) for some c>0.
ER -