This advance could help enable realistic computer simulations of more complex quantum materials, including high-temperature superconductors. In these materials, the behavior of one electron is strongly influenced by nearby electrons, making the systems difficult to describe using traditional approximations.

The researchers reported their methods and findings in a paper. The first authors are Linqing Peng (PhD ’25) and Tianyu Zhu of Yale University. Peng and Zhu both began working on the project in the laboratory of Garnet Zhang, the Bren Professor of Chemistry and director of the Rudolph A. Marcus Center for Theoretical Chemistry at Caltech.

“It is now possible to predict the properties of some complex materials purely computationally, without reference to experiments,” says Zhang, the paper’s senior author and a Simons Fellow in Physics. “These first materials we studied are like baby steps, or prototype problems, on the way to more complex phenomena such as high-temperature superconductors and quantum magnets.”

The Kondo Effect: A Classic Many-Body Physics Challenge

In many materials used in modern electronics, including semiconductors such as silicon, interactions between electrons are weak enough that they can often be ignored when describing the material’s overall behavior. That is not the case for strongly correlated materials, which are important for many proposed quantum technologies. In these systems, it is essential to understand how electrons interact and scatter.

The Kondo effect is one of the simplest examples of a strongly correlated system. It occurs when a single magnetic atom, such as iron or manganese, is placed as an impurity inside a metal such as copper. When the material is cooled below a certain temperature, known as the Kondo temperature, its electrical behavior changes in an unusual way.

Normally, when a metal is cooled, its electrical resistance gradually decreases, allowing current to flow more easily. However, in metals containing magnetic impurities, the resistance stops decreasing once the Kondo temperature is reached. After reaching a minimum, it begins to rise again as the temperature continues to fall.

“This is a characteristic of the Kondo effect, where electrons in impurities interact with electrons moving through the bulk metal,” Zhang explains.

Physicists developed the general theoretical picture of the Kondo effect in the 1970s, including Dr. Kenneth Wilson, who graduated in 1961. The phenomenon became a classic example of a many-body problem because it requires researchers to describe a huge number of interacting particles—in this case, electrons in a metal. The behavior of these particles cannot be understood by processing them one at a time.

Magnetic impurities contain unpaired electrons whose spin gives atoms their magnetic properties. At high temperatures, an atom’s magnetic direction, known as its magnetic moment, can vary freely. As the material cools, electrons moving through the surrounding metal begin to interact strongly with the impurity’s spin.

These electrons can flip their spin in a way that partially cancels the magnetic moment of the embedded atom. The additional scattering caused by these interactions produces a flattening in the material’s properties and an increase in its final electrical resistance. As more electrons join the process, they collectively surround the impurity and eventually hide its magnetism.

In effect, the surrounding electrons form a cloud that “blocks” or cancels the atom’s magnetism.

Moving Beyond Simplified Quantum Models

The Kondo effect has been extensively studied because, despite the complexity of its underlying physics, the basic problem is relatively easy to explain. It has therefore become an important benchmark for testing new theoretical and computational methods.

Until now, however, researchers have been unable to calculate precisely how the resistance of real materials drops and then rises again, or to determine the exact temperature at which that change occurs for specific impurities.

Traditional approaches simplify a material’s electronic structure by reducing it to a small set of orbitals—the regions around the nucleus where electrons are most likely to exist. Researchers then use approximate mathematical models to describe the smaller system.

Chan and his colleagues chose a different strategy. They applied high-precision computational tools originally developed in quantum chemistry to describe molecules and used them to study quantum materials. This allowed the researchers to represent magnetic impurities as if they were molecules while preserving the full complexity of their electronic interactions.

More Accurate Predictions for Real Materials

The researchers tested their method on seven different transition-metal atoms embedded in copper. For most of the factors they investigated, their calculations were two orders of magnitude more accurate than predictions from traditional model-based methods.

“We are in an exciting era, where faithful predictive quantum descriptions of the full chemical complexity of real materials are within reach,” Penn says. “For even the most difficult classes of quantum materials, it is becoming practical to predict material-specific correlated-electron behavior based on first principles.

“This is an important step toward computationally designing materials whose functionality emerges from complex, interrelated physics such as high-temperature superconductivity. In high-temperature superconductivity, the large chemical space and competition between many phases require predictive theories to help focus the experimental search for new materials,” she adds. “I’m looking forward to seeing what new material breakthroughs this theory will enable in the future.”

The authors of the California Institute of Technology paper, “Towards an Accurate Quantum Many-Body Treatment of Kondo Correlations in Magnetic Impurities,” include former postdoctoral fellow Huanchen Zhai, current postdoctoral researcher Runze Chi, and Zhi-Hao Cui (PhD ’23), who completed his research as a graduate student.

The research received support from the Air Force Office of Scientific Research through the Interdisciplinary University Research Initiatives Program, the U.S. Department of Energy and its Center for Molecular Magnetic Quantum Materials, and the U.S. National Science Foundation.