Instantaneous Response and Quantum Geometry of Insulators
We present the time-dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool for capturing the geometric character of insulators observable within linear response. We show that tQGT describes the zero-point motion of bound electrons and acts as a generating function for generalized sum rules of electronic conductivity. Therefore, tQGT enables a systematic and basis-independent framework to compute the instantaneous response of insulators, including optical mass, orbital angular momentum, and the dielectric constant in low-energy effective theories. It allows for a consistent approximation across these quantities upon restricting the number of occupied and unoccupied states in an effective low-energy description of an infinite quantum system. We outline how quantum geometry can be generated in periodic systems by lattice interference and examine spectral weight transfer from small frequencies to high frequencies by creating geometrically frustrated flat bands.
About the QSQM: The EFRC-QSQM center aims to develop and apply nontrivial quantum sensing to measure and correlate local and nonlocal quantum observables in exotic superconductors, topological crystalline insulators, and strange metals. The center is led by the University of Illinois at Urbana-Champaign in partnership with the University of Illinois at Chicago and the SLAC National Accelerator Laboratory.
