1:30 pm MCP 201
Geometry of Insulators and Topology of Metals --- An Entangled View from the Corner.
Geometry and topology are the natural languages that have long guided our understanding of the physical world. Like the manifold of spacetime, there are manifolds of quantum states realized in condensed matter platforms. In the first part of the talk, I will introduce the geometric characterization of quantum materials, known as quantum geometry, which is relevant to various exotic phenomena like unconventional superconductivity and fractional quantum anomalous Hall effect. Particularly, I will advertise a direct link between quantum geometry and the correlated charge fluctuation in generic two-dimensional insulators, including interacting systems. This connection not only provides an experimental probe of quantum geometry but also links quantum geometry to the quantum information content of an insulator, via the lens of “corner entanglement entropy”.
In the second part, I will switch gears to focus on a different class of materials: the metals. I will introduce how the correlated charge fluctuation can again capture a fundamental aspect of this quantum matter --- the Fermi sea topology. For Fermi gases, we will see how the particle-number fluctuation depends only on the genus of the Fermi sea manifold, which further determines the multipartite entanglement of the Fermi gas. Overall, I hope to convey that geometry, topology, and quantum entanglement can all be connected through the experimentally accessible quantity of charge fluctuation.