低维量子系统：精确和数值方法

Quantum physics is at the heart of an ongoing revolution of discovery. It is now commonplace for experimentalists to engineer devices on the nanoscale level and manufacture and manipulate low-dimensional quantum systems, where quantum effects can be most pronounced. These include the fabrication of magnetic impurities such as single and multiple quantum dots. In general, quantum dot devices provide strongly correlated many-body systems in which to investigate, probe and control quantum phenomena. They thus provide an ideal platform to advance the basic understanding of new quantum effects with potential applications in future generation solid-state technology. This project aims to advance the use of exact and numerical methods to study such low-dimensional quantum systems. The exact methods to be used are based on the fundamental theory of integrable quantum many-body systems solved exactly by means of the Bethe Ansatz. The exact solutions obtained in this theory will be further developed and applied in this project. The numerical methods to be used are based on powerful recent computational developments using tensor networks. In particular, the project aims to explore and exploit the recently observed connection between the Bethe Ansatz and tensor network algorithms. Tensor network algorithms will also be used to numerically investigate and explore the physics of quantum systems which are not amenable to exact solution. This will allow the investigation of multiple quantum dots in and out of equilibrium. The results from this project, in the setting of non-equilibrium quantum impurities, can be used to address major challenges in understanding the fundamental physics of quantum noise and entropy production in more general systems.

迄今为止持续不断的重要发现使量子物理这一领域一直处于物理前沿研究的核心。目前，实验物理学家能够在纳米尺度上设计和制备低维量子结构和器件，一个恰当的例子是单量子点和多量子点的磁性杂质的制备。在这个数量级上必然涉及量子效应，因此通常将这一类的结构叫量子器件。一般地讲，量子点器件提供了可用于研究、探索和控制量子现象的强关联多体系统，成为理解和探索各种新颖量子效应的理想平台，能帮助我们深刻理解下一代固体技术的本质和潜在应用。. 本项目拟发展可用于研究这类低维量子结构的精确和数值方法，即可积系统的Bethe Ansatz方法和近年已取得巨大进展的、功能强大的张量网络算法。这将允许对于平衡和非平衡多量子点问题进行深入彻底的研究。我们期望，本项目有关非平衡量子杂质的研究成果可用于理解一般系统内普遍存在的量子噪声和熵产生的基本物理机制，并应对其面临的主要挑战。

本项目研究了多个低维量子系统的物理性质，包括相图，量子临界性，关联和热力学性质。其中主要使用了量子保真度和几何纠缠等为基础开展研究以得到新的视角。借助现代物理中心已有的计算机集群和算法，本项目实现了精确解和数值计算的结合研究。研究的模型包括：量子自旋梯子模型、一维量子自旋链、二维量子自旋模型、自由仲费米子链、量子Hubburd链和量子Rabi模型的扩展模型。相关研究成果已公开发表于6 篇期刊论文。