The Quantum Geometric Tensor: Novel Applications in Isolated Quantum System
This event is part of the Departmental Seminars.
Dissertation Committee: Anatoli Polkovnikov, Claudio Chamon, Shyam Erramilli, Alexander Sushkov, Pankaj Mehta
Geometric ideas always played an important role in the understanding and the unication of physical phenomena. The main objective of this talk is to highlight several novel geometrical and topological properties of isolated quantum systems characterized by the quantum geometric tensor. First, we show how the knowledge of such properties allows one to explore topologically protected regions by adiabatically breaking and re-establishing symmetries. Next, by calculating shortest paths between dierent points in Hilbert space, we develop optimal protocols for adiabatic state preparation, which were used in recent experiments with superconducting qubits. These geodesic paths are shown to optimize important quantities such as the mean delity and squared energy variance. Further, we establish how topological charges are protected and what that means for the topological characteriza- tion of dierent Hamiltonians. Finally, we discuss the logarithmic divergence of the quantum geometric tensor with respect to the system size. A similar divergence behavior is observed for the entanglement entropy in conformal eld theories and also for the entropy of black-holes.