MURAL - Maynooth University Research Archive Library



    Dynamics and level statistics of interacting fermions in the lowest Landau level


    Fremling, M. and Repellin, Cécile and Stéphan, Jean-Marie and Moran, N. and Slingerland, Joost and Haque, Masud (2018) Dynamics and level statistics of interacting fermions in the lowest Landau level. New Journal of Physics (NJP), 20 (103036). ISSN 1367-2630

    [img]
    Preview
    Download (2MB) | Preview


    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...



    Add this article to your Mendeley library


    Abstract

    We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g. in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian orthogonal ensemble) can appear in many cases despite the lack of time-reversal symmetry.

    Item Type: Article
    Additional Information: Cite as: M Fremling et al 2018 New J. Phys. 20 103036. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. https://creativecommons.org/licenses/by/3.0/
    Keywords: fractional quantum Hall effect; integrability; level statistics; time evolution; Landau levels; non-comutative geometry;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10529
    Identification Number: https://doi.org/10.1088/1367-2630/aae73f
    Depositing User: Dr. Joost Slingerland
    Date Deposited: 21 Feb 2019 10:47
    Journal or Publication Title: New Journal of Physics (NJP)
    Publisher: Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft
    Refereed: Yes
    URI:

    Repository Staff Only(login required)

    View Item Item control page

    Downloads

    Downloads per month over past year