Exploration of classical-quantum and easy-hard boundaries

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

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.