The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions. We identify and resolve key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, we study the dynamics of the paradigmatic two-dimensional transverse field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium real-time evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

中文翻译：

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人工神经网络在二维量子多体动力学中的应用

在孤立的量子物质中非平衡实时演化的有效数值模拟构成了当前计算方法的关键挑战。这尤其在两个空间维度的体系中成立，目前在量子模拟器中大力进行了其实验探索。在这项工作中，我们基于最近引入的对量子多体波函数进行编码的人工神经网络，提出了一种通用且有效的机器学习启发方法。我们确定并解决了模拟时间演化的主要挑战，这些挑战以前曾对大型系统和长时间动态的精确描述施加了重大限制。作为一个具体的例子，我们研究了典型的二维横向场伊辛模型的动力学，最近在里德堡原子系统中也通过实验实现了这一点。计算广泛参数范围内的非平衡实时演化，例如，我们观察到铁磁阶的崩溃和复兴振荡，并证明所达到的时标可与甚至超过最新的张量网络方法。