Unification of Topological Invariants and Topological Markers

Explore the unification of topological invariants and topological markers in this 42-minute conference talk by Wei Chen from PUC-Rio, Brazil. Delivered at the Workshop on Strong Electron Correlations in Quantum Materials: Inhomogeneities, Frustration, and Topology, delve into key concepts such as wrapping numbers, quantum metrics of filled band states, and time-dependent perturbation theory. Examine applications in graphene and investigate local and nonlocal topological markers in 1D and 2D classes. Gain insights into patterns of topological invariants and discover intriguing applications of quantum metrics in this comprehensive presentation on quantum materials and topology.

Intro
Outline
Some patterns for the topological invariants
Introducing the wrapping number (a.ka. degree of the map)
Quantum metric of (degenerate) filled band states
Time-dependent perturbation theory of measuring quantum metric
Estimation for graphene
Other intriguing applications of quantum metric
Local and nonlocal topological marker
Applications to 1D classes
Summary
Applications to 2D classes