Bruno Nachtergaele

University of California, Davis

https://www.math.ucdavis.edu/~bxn/ 

Speaker at the Spring Time in Mathematical Quantum Physics Workshop ( UBC, May 2025)

Title: The Charge Gap, the Neutral Gap, and Fractional Quantum Hall Systems.

Abstract: We introduce an elementary inequality relating the charge and neutral gaps of a family of quantum many-body systems and discuss an application to the so-called pseudo-potentials modeling fractional quantum Hall systems. These 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 general inequality can be refined, opening the possibility of new applications to the study of the spectral gap of such systems.   
(Joint work with Marius Lemm, Simone Warzel, and Amanda Young, arxiv:2410.11645).

Bruno Nachtergaele
Scientific, Workshop
Spring Time in Mathematical Quantum Physics
May 5–9, 2025
University of British Columbia
The Spring Time in Mathematical Quantum Physics workshop gathers leading experts and emerging researchers to explore analytical and topological aspects of many-body quantum mechanics. Discussions will cover topics such as the effective macroscopic...
Scientific, Seminar
Diff. Geom, Math. Phys., PDE Seminar: Bruno Nachtergaele
March 20, 2018
University of British Columbia
Kitaev’s quantum double models provide a rich class of examples of two-dimensional lattice models with topological order in the ground states and a spectrum described by anyonic elementary excitations. The infinite volume ground states of the abelian...