PIRSA:25020032

The Charge Gap exceeds the Neutral Gap in Fractional Quantum Hall Systems

Nachtergaele, B. (2025). The Charge Gap exceeds the Neutral Gap in Fractional Quantum Hall Systems. Perimeter Institute. https://pirsa.org/25020032

Nachtergaele, Bruno. The Charge Gap exceeds the Neutral Gap in Fractional Quantum Hall Systems. Perimeter Institute, Feb. 13, 2025, https://pirsa.org/25020032 

          @misc{ pirsa_PIRSA:25020032,
            doi = {},
            url = {https://pirsa.org/25020032},
            author = {Nachtergaele, Bruno},
            keywords = {Condensed Matter},
            language = {en},
            title = {The Charge Gap exceeds the Neutral Gap in Fractional Quantum Hall Systems},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {feb},
            note = {PIRSA:25020032 see, \url{https://pirsa.org}}
          }

Bruno Nachtergaele University of California, Davis

Talk numberPIRSA:25020032
Collection
Talk Type Other
Subject

Abstract

The so-called pseudo-potentials modeling fractional quantum Hall systems are quantum many-body Hamiltonians that are frustration free and have two symmetries, one related to the conservation of charge (particle number) and another to the conservation of dipole moment (angular momentum), in addition to translation invariance. We show that for such systems the minimum energy of charged excitations is bounded below by the minimum energy of neutral excitations. This property, which had been repeatedly observed in numerical simulations, has a surprisingly simple proof (joint work with Marius Lemm, Simone Warzel, and Amanda Young, arxiv:2410.11645).