Quantum simulation has been developed extensively over the past decades, widely applied to different models to explore dynamics in the quantum regime. Rydberg atoms have strong dipole–dipole interactions and interact with each other over a long distance, which makes it straightforward to build many-body interacting quantum systems to simulate specific models. Additionally, neutral atoms are easily manipulated due to their weak interactions. These advantages make Rydberg many-body system an ideal platform to implement quantum simulations. This paper reviews several quantum simulations for different models based on Rydberg many-body systems, including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism, XY model for excitation transport, SSH model for symmetry-protected topological phases, and critical self-organized behaviors in many-body systems. Besides, some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper.

在过去的几十年中，量子模拟得到了广泛的发展，广泛应用于不同的模型以探索量子体系中的动力学。里德堡原子具有强烈的偶极-偶极相互作用，并且在长距离内相互作用，这使得构建多体相互作用量子系统来模拟特定模型变得简单。此外，由于它们的弱相互作用，中性原子很容易被操纵。这些优势使里德堡多体系统成为实现量子模拟的理想平台。本文回顾了基于里德堡多体系统的不同模型的几种量子模拟，包括一维量子伊辛模型和主要用于量子磁学的二维量子模型，XY激发传输模型、对称保护拓扑相的 SSH 模型以及多体系统中的关键自组织行为。此外，本文还讨论了基于里德堡多体系统的量子模拟的一些挑战和有前景的方向。