Machine learning approach to dynamical properties of quantum many-body systems
Machine learning approach to dynamical properties of quantum many-body systems
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DOI：
10.1103/physrevb.100.245123
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发表时间：
2019-07
影响因子：
3.7
通讯作者：
D. Hendry;A. Feiguin
中科院分区：
文献类型：
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作者：
D. Hendry;A. Feiguin
量子态的变分表示有很多，并已成功地用于猜测量子多体系统的基态性质。有些是基于部分物理洞察（例如，Jastrow，Gutzwiller投影和分数量子霍尔态），而其他人则作为一个黑盒子，可能包含有关纠缠和相关性的底层结构（张量网络，神经网络）的信息，并提供了大量可以有效优化的变分参数的优势。然而，使用变分方法来研究激发态，特别是计算激发光谱，仍然是一个挑战。本文提出了一种在频域中计算量子多体系统动力学性质和谱函数的变分方法，其中问题的绿色函数被编码成一个限制玻尔兹曼机（RBM）的形式.我们引入了一个自然梯度下降法来求解线性方程组，并使用蒙特卡罗方法来获得动态相关函数。此外，我们提出了一种策略，以规范的结果，大大提高了准确性。作为例子，我们研究了一维J_1-J_2$ Heisenberg模型的动力学自旋结构因子.该方法具有一般性，并可推广到其它变分形式。
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.