人工神经网络的广义转移矩阵状态
Generalized Transfer Matrix States from Artificial Neural Networks
摘要：
确定变分波函数，有效地参数化的物理相关的状态在指数大希尔伯特空间是解决量子多体问题的关键任务之一。在这种情况下，强大的工具，如张量网络状态最近得到了来自人工神经网络（ANN）的状态的补充。在这里，我们提出并研究了一个新的量子态族，即广义转移矩阵态（GTMS），它在深度人工神经网络的框架内连接了上述两种方法。特别是，我们通过一个建设性的嵌入，GTMS类包含通用矩阵产品状态，而在同一时间能够捕获更多的长程量子相关性，超越了面积定律的纠缠张量网络的属性。虽然通用深度ANN的状态幅度无法精确评估，但GTMS网络的状态幅度可以使用传递矩阵方法进行分析计算。通过数值模拟，我们展示了GTMS网络如何在监督学习方案中学习随机矩阵乘积状态，以及如何通过长程耦合来增强网络，从而导致体积律纠缠缩放的发生。通过一个显式的例子，使用变分蒙特卡罗，我们还表明，GTMS可以参数化临界量子多体基态，以良好的精度。我们的研究结果表明，GTMS是一个有前途的候选人的临界和动力学量子多体系统的研究。
英文摘要：
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this context such as tensor network states have recently been complemented by states derived from artificial neural networks (ANNs). Here, we propose and investigate a new family of quantum states, coined generalized transfer matrix states (GTMS), which bridges between the two mentioned approaches in the framework of deep ANNs. In particular, we show by means of a constructive embedding that the class of GTMS contains generic matrix product states while at the same time being capable of capturing more long-ranged quantum correlations that go beyond the area-law entanglement properties of tensor networks. While the state amplitude of generic deep ANNs cannot be exactly evaluated, that of a GTMS network can be analytically computed using transfer matrix methods. With numerical simulations, we demonstrate how the GTMS network learns random matrix product states in a supervised learning scheme, and how augmenting the network by long-ranged couplings leads to the onset of volume-law entanglement scaling. By means of an explicit example using variational Monte Carlo, we also show that GTMS can parametrize critical quantum many-body ground states to a good accuracy. Our findings suggest that GTMS are a promising candidate for the study of critical and dynamical quantum many-body systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
