Analyzing the structure of quantum states can be done with the help of topology and entanglement. Researchers from the University of Pennsylvania wrote a paper about a relationship between the two.
Charles Kane is the Christopher H. Browne distinguished professor of physics at the University of Pennsylvania. A way in which quantum states can exhibit non-local correlations, where something that happens in one point in space is correlated with something that happens in another, is called a conceptual link between the two. There's a situation where those concepts are intertwined.
Kane spent a lot of time in his home office during the Pandemic thinking about new ideas. He imagined the classic textbook image of the Fermi surface of copper, which shows the metal's potential electron energies. Every physics student sees that picture and Kane was familiar with it.
Kane says that he learned about the picture in the 1980s, but never considered it to be a topological surface.
Kane says to think about the difference between a donut and a sphere. There is a difference. There is a hole. Topology looks at the generalizable properties of a surface. Coffee cups and donuts have the same property.
The number of holes associated with the Fermi surface of copper is four, a figure also known as a genera. Kane wondered if there was a relationship between the genus and quantumentanglement after he thought of the Fermi surface in this way.
Kane had a graduate student and an assistant professor of physics look into the possibility of a connection. They came up with a mathematical relationship between the Fermi surface and the mutual information. There are correlations that can occur in different parts of space at the same time. The exact connection between the two was provided by a number called the Euler characteristic.
The researchers extended their analysis to show that the connection was still present even when the electrons interacted with more complexity.
Kane thinks that the theoretical work done on metals will apply to other materials, such as those that involve strong interactions between electrons.
Kane says that this may allow us to come up with new ways of thinking about phases of matter that we don't understand very well. People are trying to figure out how to use quantum mechanics. When you have a lot of freedom, you have to understand how quantum mechanics work. This work is nudging us in the right direction.
In follow-up work, Kane and colleagues hope to design experiments that continue to explore the newfound link, and perhaps come up with a way to probe the structure of quantumentanglement.
More information: Pok Man Tam et al, Topological Multipartite Entanglement in a Fermi Liquid, Physical Review X (2022). DOI: 10.1103/PhysRevX.12.031022 Journal information: Physical Review X
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