Physics Seminar by Menderes Iskin

The so-called quantum geometric tensor is one of the basic components of the geometric quantum mechanics, i.e., a complex valued matrix whose real and imaginary parts are known, respectively, as the Fubini-Study or the quantum metric tensor and Berry curvature.As the naming suggests, the quantum metric is a measure of the distance between two nearby quantum states, characterized by the local geometry of the complex quantum space. In contrast, the Berry curvature corresponds to the emergent gauge field in the quantum space, the total flux of which is related to the global topology of the quantum states, e.g. the Chern number. In striking contrast to the physical importance of the Berry curvature and quantum topology that has been put forward in the past two decades or so, there is relatively much slower progress in showing the possible connection between a physical system and its quantum metric and quantum geometry. In this talk I will present an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states in a multiband Hubbard model, and discuss its possible ramifications in superluids and superconductors.

Face to face

Lifelong Learning