2023/03/03 by Adrien Bouhon, Bouhon, Adrien, Abigail Timmel +3 · 17 citations
Computer Science · Mathematics · Physics and Astronomy · #A priori and a posteriori #Computational Physics and Python Applications #Computer science #FOS: Physical sciences #Geometry #High Energy Physics - Theory (hep-th) #Mathematics #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Quantum mechanics #Strongly Correlated Electrons (cond-mat.str-el) #Text Readability and Simplification #Theoretical physics #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2303.02180
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multi-band paradigm still promises a new field of interest. Formally, multi-band systems, featuring in particular degeneracies, have been related to projective spaces, explaining also the success of relating quantum geometrical aspects of flat band systems, albeit usually in the single band picture. Here, we propose a different route involving Plücker embeddings to represent arbitrary classifying spaces, being the essential objects that encode all the relevant topology.This paradigm allows for the quantification of geometrical quantities directly in readily manageable vector spaces that a priori do not involve projectors or the need of flat band conditions. As a result, our findings are shown to pave the way for identifying new geometrical objects and defining metrics in arbitrary multi-band systems, especially beyond the single flatband limit, promising a versatile tool that can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations.