The Physics Colloquium: Peter Abbamonte (University of Illinois Urbana-Champaign) "A Peculiar Connection Between Quantum Entanglement and Wave Function Geometry in Matter"

One of the major developments in condensed matter physics over the past decade has been the realization that materials can be classified by the topology of their electronic energy bands. Originally developed for noninteracting electrons, theorists have recently generalized these concepts to interacting, many-body systems by defining a quantity called the quantum geometric tensor, which characterizes both the topology and the spatial nonlocality of a many-body wave function.

Meanwhile, researchers in quantum information science were pursuing a seemingly unrelated question: How much quantum information is contained in a physical system, whether a quantum computer, a molecule, or a piece of ordinary matter? One way to quantify this is through the quantum Fisher information (QFI), which measures both the information content and the degree of entanglement in a multipartite quantum system.

In this talk, I will show that QFI and quantum geometry are related. In an insulating system at zero temperature, the QFI associated with charge fluctuations is directly proportional to the real part of the quantum geometric tensor, known as the quantum metric. This implies a fundamental connection between quantum information, the spatial structure of many-body wave functions, and the geometry of quantum states.

Finally, I will demonstrate these relationships using inelastic x-ray scattering measurements of the dynamic charge susceptibility of two garden-variety insulators, lithium fluoride and diamond. The susceptibility provides a direct measurement of both the quantum metric and QFI, allowing us to compare the information content of these materials. We find that diamond, a covalently bonded solid, exhibits greater quantum nonlocality and a higher information density than LiF, an ionic solid, suggesting a connection between quantum information and chemical bonding. I will also show that our measurements satisfy fundamental bounds predicted by Bradlyn, Fu, Martin, and others from quantum geometric sum rules. I will close by discussing how quantum geometry can provide new insights into the properties of interacting quantum matter.