Exploration of classical-quantum and easy-hard boundaries

量子自旋就像经典磁铁一样，可以指向任何方向，但量子自旋的集合通常表现出更奇特的方式，可以指向比经典自旋更多的方向。这通常意味着量子多体问题比经典问题要难得多。然而，在一些物理模型中，尽管量子自旋可以指向更多方向(源于较大的自旋量)，但事实证明，它们的行为很像经典磁铁，只是在它们指向的方向上有很小的波动。似乎即使在量子世界中，也有一些区域看起来或多或少像经典世界。经典领域和量子领域之间的边界在哪里？量子问题什么时候变得容易，什么时候变得难？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。将该项目的研究成果整合到量子信息和量子多体物理的教育中，将有助于培养具有新思维工具的新一代学生。该项目还包括培训一名研究生和指导一名博士后研究员。计划的外展活动，如公开讲座、指导高中生的暑期研究项目、为高中生编写科学和数学教育材料和活动等，将补充研究活动并产生持续的影响。

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.