Condensed Matter Theory Seminar - Alexander Avdoshkin - “Extrinsic geometry of quantum states”

Event time: 
Thursday, January 18, 2024 - 1:00pm to 2:00pm
Sloane Physics Laboratory SPL, Room 51 See map
217 Prospect Street
New Haven, CT 06511
Alexander Avdoshkin - MIT
Event description: 

A quantum state that depends on a parameter is a commonly studied structure in quantum physics. Bloch states, as functions of the quasimomentum, provide one prominent example. The change in the state as the parameter varies is commonly characterized by geometric objects such as the Berry phase or the quantum distance, leading to many insights in the understanding of quantum systems. These objects are the main tools in our understanding of topology in solid-state systems, as well as properties of correlated states in flat bands.

In the talk, I will present a general framework for describing the geometric invariants of a manifold of quantum states (e.g., Brillouin zone) that produces all known objects and also leads to some new ones that we call extrinsic. The simplest extrinsic object takes the form of a symplectic connection, and I will discuss its importance for non-linear optics. The talk is based on arXiv:2205.15353.