标题： 一种机器学习方法用于量子多体系统的动力学性质 显示英文标题

标题： A machine learning approach to dynamical properties of quantum many-body systems

摘要： 变分表示的量子态很多，并且已经被成功用于猜测量子多体系统的基态性质。 一些方法基于部分物理直觉（例如Jastrow、Gutzwiller投影和分数量子霍尔态），而其他方法则作为黑箱操作，可能包含关于纠缠和相关性底层结构的信息（如张量网络、神经网络），并且具有可以高效优化的大规模变分参数集的优势。 然而，使用变分方法研究激发态，特别是计算激发谱，仍然是一个挑战。 我们提出了一种变分方法，在频域中计算量子多体系统的动态性质和谱函数，其中问题的格林函数以受限玻尔兹曼机（RBM）的形式编码。 我们引入了一种自然梯度下降方法来求解线性方程组，并使用蒙特卡罗方法获得动态关联函数。 此外，我们提出了一种改进结果准确性的正则化策略。 作为示例，我们研究了一维$J_1-J_2$ Heisenberg 模型的动力学自旋结构因子。 该方法是通用的，可以扩展到其他变分形式。 显示英文摘要

摘要： Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional $J_1-J_2$ Heisenberg model. The method is general and can be extended to other variational forms.