Transport in Quantum Spin Systems

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This award will fund research on topological phases of quantum matter, an interdisciplinary research area encompassing physics, computer science, and mathematics. A longstanding goal of this field is to produce novel materials with properties that are inherently immune to defects and noise. For example, they can carry electrical currents that do not decay in time and do not introduce errors in computations based on their topological properties, prioritizing them for the construction of quantum computers. Primary investigators (PIs) will develop a mathematical theory to understand the properties of such materials better, especially how to classify them and how to quantify their robustness to defects. The students working on the project will work alongside the PIs and gain expertise in the area. Developing a pool of young people proficient in quantum mechanics is a crucial part of quantum leap, and the award will help to build this pool through students' apprenticeships. Integer Quantum Hall effect is the primary example of a topological phase of matter. The mathematical theory of Quantum Hall effect in the absence of interactions was developed in the 1980s and 1990s. In recent years there was a strong push to develop the tools in the presence of interactions with the potential of extending the theory to topological phases requiring interactions. This award will merge two prominent directions in this research, many-body localization, and many-body index theory. PIs aim to show that the recently constructed indices are robust to many-body localization, both as mathematical and physical indices, which means that they are integer valued and constant in each topological phase and that they retain the meaning of electrical conductance. This task requires a better understanding of the transport properties of disordered many-body systems than is currently available. Study of these properties is another focus of the project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.