Abstract
We review recent results concerning the localization of gapped periodic systems of independent fermions, as, e.g., electrons in Chern and Quantum Hall insulators. We show that there is a “localization dichotomy” which shows some analogies with phase transitions in Statistical Mechanics: either there exists a system of exponentially localized composite Wannier functions for the Fermi projector, or any possible system of composite Wannier functions yields a diverging expectation value for the squared position operator. This fact is largely model-independent, covering both tight-binding and continuous models. The results are discussed with emphasis on the main ideas and the broader context, avoiding most of the technical details.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.