Quantum Hall states in optical lattices : Revealing hidden long-range

Abstract :

The study of interacting quantum Hall states and their exotic anyonic excitations poses a major challenge in current experimental and theoretical research. Quantum simulators, in particular cold atoms in optical lattices, provide a promising platform to realize, manipulate, and understand such systems with unprecedented control. In this talk, I will discuss how the local resolution of quantum gas microscopes extends the toolbox of quantum Hall physics. To this end, I will discuss a fundamental question regarding the topological order of quantum Hall states: the speculated condensation of composite bosons exhibiting quasi long-range order. I will exemplify this mechanism in bosonic [1] and fermionic [2] systems and touch upon its detectability in tensor network simulations and quantum gas microscopes. If time permits, I will also touch upon the interplay of spin and charge in fermionic quantum Hall states, resulting in ferromagnetism and skyrmionic spin-textures [2,3]. Again, I will present signatures to identify these states in cold-atom quantum simulators. References : [1] Pauw et al., Detecting Hidden Order in Fractional Chern Insulators; PRR 6 (2024) [2] Pauw et al., From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model; arXiv:2509.12184 (2025) [3] Palm et al., Ferromagnetism and skyrmions in the Hofstadter–Fermi–Hubbard model; NJP 25 (2023) Contact : cecile.repellin@lpmmc.cnrs.fr