Finite-Size Criteria for Spectral Gaps in Quantum Lattice Systems (A08)

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

This project is devoted to finite-size criteria for deriving spectral gaps in quantum spin systems and other quantum lattice models. We aim to significantly expand the scope of finite-size criteria by proving new criteria for long-ranged and unbounded interactions which arise for example in bosonic lattice gases. Moreover, we plan to apply finite-size criteria to derive spectral gaps for concrete Hamiltonians of interest, such as Motzkin spin chains, the AKLT Hamiltonian on the square lattice, and long-ranged bosonic lattice gases. To achieve these goals, we will draw, among other things, on recent developments for deriving and applying finite-size criteria by using interaction weights and on analytical tools for estimating bosonic operators.

• 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