可积砖墙电路中算子纠缠的平方根增长
Square-root growth of operator entanglement in an integrable brickwork circuit
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中文总结 AI 辅助
该研究通过四态砖墙电路中的置换矩阵门构造反例，证明可积系统中算子纠缠可平方根增长，并指出模拟所需键维指数增长。
中文摘要 AI 辅助
普遍预期在无穷体积的可积多体系统中，局域算子的冯·诺依曼纠缠最多呈对数增长。我们给出了一个反例：一个四态砖墙电路，其门是求解常数杨-巴克斯特方程的置换矩阵。冯·诺依曼算子熵增长为 $(\log2)\sqrt{t/\pi}+O(\log t)$，而固定指标的Rényi熵在指标低于1时线性增长，高于1时对数增长。在固定的相对希尔伯特-施密特误差低于1时，矩阵乘积态模拟所需的键维至少以 $\exp(c\sqrt t)$ 增长，其中 $c>0$。
英文摘要
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 $(\log2)\sqrt{t/π}+O(\log t)$, 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 $\exp(c\sqrt t)$ for some $c>0$.
发表机构
- MTA-ELTE ``Momentum'' Integrable Quantum Dynamics Research Group, ELTE E\"otv\"os Lor\'
- University, Budapest, Hungary
机构由 AI 辅助整理，请以论文原文为准。
