How localized is an extended quantum system ?
Abstract
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, zL, is introduced to study the localization properties of extended quantum systems. zL, which allows us to discriminate between conducting and non-conducting thermodynamic phases, has an illuminating physical (and geometric) interpretation. Its phase can be related to the expectation value of the position operator (and a Berry phase), while its modulus is associated with quantum electric polarization fluctuations (and a quantum metric). We also study the scaling behavior of zL in the one-dimensional repulsive Hubbard model.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.