Schmitt Markus, Heyl Markus
Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Phys Rev Lett. 2020 Sep 4;125(10):100503. doi: 10.1103/PhysRevLett.125.100503.
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 timescales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.
孤立量子物质中非平衡实时演化的高效数值模拟是当前计算方法面临的一项关键挑战。这在二维空间领域尤为如此，目前人们正在量子模拟器中大力开展对其的实验探索。在这项工作中，我们基于最近引入的量子多体波函数的人工神经网络编码，提出了一种通用且高效的受机器学习启发的方法。我们识别并解决了时间演化模拟中的关键挑战，这些挑战此前对大型系统和长时间动力学的精确描述造成了重大限制。作为一个具体例子，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该模型。通过计算广泛参数范围内的非平衡实时演化，例如，我们观察到铁磁序的坍缩和复苏振荡，并证明所达到的时间尺度与最先进的张量网络方法相当或超过了其能力。
