Abstract
The geometrical structure of Quantum State Manifolds of parametric Hamiltonian systems has implications in many fields, such as the theory of Phase transitions or in the decohering quantum state driving. However, its precise meaning remains unknown.
Our research aims on explaining the physical meaning of this geometrical structure, especially on the Fubini-Study metric. As a numerical model, we utilize a fully-connected qubit model, a special form of a Lipkin-Meshkov-Glick model, for which the quantum phase transitions are well observed.