Mariusz Adamski

From Quantum Geometry to Phase Transitions

I will briefly introduce some quantum-geometrical concepts, such as fidelity and quantum geometric tensor, and show how they can be used in the studies of quantum phase transitions. Next, I will skim through some of my own results in a particular two dimensional model, which can be regarded as a mean field approximation to the so-called t-J model, postulated as the one describing high temperature superconductivity (at last in cuprates). We will see how those geometric methods work in practice, which will also enable us to postulate some "heuristic" and not-so-heuristic rules that govern this approach.