Localization and Delocalization Phenomena in Interacting Many-Particle Systems

About This Grant

This project explores (de-)localization phenomena in interacting many-particle systems, in particular quantum mechanical spin systems. Whether such a system is (de-)localized can have important implications in fields like quantum computing, where it is essential to control undesirable phenomena such as decoherence due to interactions of the states in a quantum computer with its environment. One indicator of a system being (de-)localized is the scaling behavior of the entanglement entropy between that system and its environment, which is the main focus of this project. In addition, the recently founded Baylor Math Circle, an after-school math enrichment program targeted at middle-school aged children in the Waco area, will be continued through the period of this grant with the objective to design and deliver regular workshop activities for interested children. The main goal will be increased involvement and future access to STEM careers. A college mentoring program connecting local families with current Baylor students will be launched during the third year of the project. The project will contribute to the rigorous understanding of many-body (de-)localization phenomena in interacting many-particle quantum systems. An important measure of the correlation structure of a quantum state is the scaling behavior of its bipartite entanglement entropy. Currently, few results for interacting many-particle systems are known, and none in higher dimensions. The purpose of this project is to analyze the scaling behavior of the entanglement entropy of localized and delocalized physical systems of interacting particles with particular focus on (i) droplet states in disconnected subsystems, (ii) higher-energy states beyond the droplet spectrum, and (iii) systems defined on higher-dimensional lattices. In addition, the transport velocity in models with large potentials that exhibit delocalization will be studied to further provide more quantitative statements about quantum transport. 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.