Exploration of classical-quantum and easy-hard boundaries

一个量子自旋，就像一个经典的磁铁，可以指向任何方向，但是量子自旋的集合通常表现得更奇特，可以比经典自旋指向更多的方向。这通常转化为量子多体问题比经典问题更难的特征。然而，在一些物理模型中，量子自旋，即使它们可以指向更多的方向（这源于大的自旋量级），结果却表现得很像经典磁铁，在它们指向的方向周围只有很小的波动。似乎即使在量子世界中，也有一些区域看起来或多或少与经典世界相似。经典领域和量子领域的边界在哪里？量子问题什么时候变得容易，什么时候变得困难？这两个密切相关的问题是这个项目的主题。对这种“跃迁”的清晰描述将有助于理解量子多体系统的奇异特性。将本项目的研究成果整合到量子信息和量子多体物理教育中，将有助于培养具有新思维工具的新一代学生。该项目还包括培养一名研究生和指导一名博士后研究员。公开演讲、高中生暑期研究课题指导、开发高中生科学、数学教育教材和活动等外展活动将对研究活动起到补充作用，并产生持久的影响。

A quantum spin, like a classical magnet, can point at any direction, but a collection of quantum spins generally behave in a more exotic way and can point to many more directions than classical spins do. This usually translates to the feature that quantum many-body problems are much harder than classical problems. However, in some physical models, quantum spins, even though they can point to more directions (which originate from large spin magnitudes), turn out to behave much like classical magnets, with only small fluctuations around the direction they point to. It seems that even in the quantum world, there are regions that look more or less like the classical world. Where is the boundary between the classical and quantum territories? When do quantum problems become easy and when do they become hard? These two intimately related questions are the subject of this project. A clear characterization of such a `transition' will help to understand the exotic properties of quantum many-body systems.The integration of the research findings of this project into education on quantum information and quantum many-body physics will help to nurture a new generation of students with new tools of thinking. This project also includes training of a graduate student and mentoring of a postdoctoral researcher. The planned outreach activities such as giving public lectures, mentoring high school students for summer research projects, and developing materials and activities for high school students in science and mathematics education will complement the research activities and lead to sustaining impacts.