Unified theory of mobile and static impurities connects fundamental domains of modern quantum physics

A new unified theory connects two fundamental domains of modern quantum physics: It joins two opposite views of how a single exotic particle behaves in a many-body system, namely as a mobile or static impurity among a large number of fermions, a so-called Fermi sea. This new theoretical framework was developed at the Institute for Theoretical Physics of Heidelberg University. It describes the emergence of what is known as quasiparticles and furnishes a connection between two different quantum states that, according to the Heidelberg researchers, will have far-reaching implications for current quantum matter experiments.

Differing views prevail in quantum many-body physics on how impurities, i.e., exotic electrons or atoms, behave among many other particles. According to the established quasiparticle model, a single particle moves through a sea of fermions, such as electrons, protons, or neutrons, and interacts with its neighbors. It drags these surrounding particles along, forming a new composite object known as a Fermi polaron, a quasiparticle that behaves like an individual particle but emerges from the coordinated movement of the impurity and the particles interacting with it. The quasiparticle model has become a cornerstone for understanding strongly interacting systems, from cold atomic gases to solid-state and nuclear matter, as Eugen Dizer, a doctoral candidate at the Institute for Theoretical Physics at Heidelberg University, explains.

Standing in contrast is a phenomenon known as Anderson’s orthogonality catastrophe. It occurs when an impurity is extremely heavy and effectively immobile, which changes the many-body system dramatically. The wave functions of the fermions are modified so much that they completely lose their original character and form a complex background that prevents coordinated movement and thus the emergence of quasiparticles. With the help of various analytical methods, the Heidelberg researchers have succeeded in harmonizing these two descriptions of mobile and static impurities in quantum systems. For decades, physicists have lacked a theory connecting these two states.

“The theoretical framework we developed explains how quasiparticles emerge in systems with an extremely heavy impurity, connecting two paradigms that have long been treated separately,” explains Eugen Dizer, a member of the Quantum Matter Theory working group led by Prof. Dr Richard Schmidt. Underlying the new theory is the finding that even very heavy impurities perform slight motions when their environment adjusts. This opens an energy gap, allowing quasiparticles to emerge from the complex, strongly correlated background. The Heidelberg researchers showed that this mechanism naturally explains the transition from so-called polaronic to molecular quantum states.

According to Prof. Schmidt, these latest research results provide a powerful description of impurities that can be extended to different spatial dimensions and various types of interactions. “Our research not only advances the theoretical understanding of quantum impurities but is also directly relevant for ongoing experiments with ultracold atomic gases, two-dimensional materials, and novel semiconductors,” adds the Heidelberg physicist.

The research was carried out under the auspices of Heidelberg University’s STRUCTURES Cluster of Excellence as well as the ISOQUANT Collaborative Research Centre 1225. The results were published in the journal “Physical Review Letters”.