用自回归网络直接计算量子自旋链的纠缠熵，高效准确。
Estimation of the reduced density matrix and entanglement entropies using autoregressive networks
- 用自回归网络估计连续自旋的条件概率，直接计算约化密度矩阵元。
- 在伊辛链上算出最多5个自旋区间的冯诺依曼与瑞尼纠缠熵的连续极限。
- 单次训练即可适用于不同参数，适合研究热态和带缺陷体系。
我们将自回归神经网络应用于量子自旋链的蒙特卡洛模拟，利用其与经典二维自旋系统之间的对应关系。通过一系列能够估计连续自旋条件概率的神经网络，直接计算约化密度矩阵的矩阵元。以伊辛链为例，我们计算了由最多5个自旋组成的区间在基态下的冯诺依曼与瑞尼纠缠熵的连续极限。结果表明，该架构仅需一次训练即可在固定时间离散化和晶格体积下准确估计所有所需矩阵元。该方法可推广至其他类型的自旋链，包括存在缺陷的情况，以及非零温度热态的纠缠熵估计。
原文摘要 · Abstract (English)
We present an application of autoregressive neural networks to Monte Carlo simulations of quantum spin chains using the correspondence with classical two-dimensional spin systems. We use a hierarchy of neural networks capable of estimating conditional probabilities of consecutive spins to evaluate elements of reduced density matrices directly. Using the Ising chain as an example, we calculate the continuum limit of the ground state's von Neumann and Rényi bipartite entanglement entropies of an interval built of up to 5 spins. We demonstrate that our architecture is able to estimate all the needed matrix elements with just a single training for a fixed time discretization and lattice volume. Our method can be applied to other types of spin chains, possibly with defects, as well as to estimating entanglement entropies of thermal states at non-zero temperature.
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