Low-Energy States and Spectra of Quantum Hall Systems (A07)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 470903074

In this project, we analyze Haldane pseudopotentials which are commonly used in a Hamiltonian description of fermionic or bosonic systems of Quantum Hall nature. In particular, we aim to provide a mathematically complete and effective description of their ground states. The main long-term goal is to prove a spectral gap for these many-particle operators and to study properties of excitations. Progress will be made by using a coherent state approach and by developing stability methods starting from truncated pseudopotentials.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 352: Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
• Applicant Institution: Ludwig-Maximilians-Universität München
• Project Heads: Marius Lemm; Professorin Dr. Simone Warzel