A new computational approach uses the real electronic structure of materials to predict a classic quantum effect far more accurately than simplified models.
Seven magnetic atoms embedded one at a time in copper have given physicists a new way to test whether computers can predict the behavior of real quantum materials without first reducing them to simplified models.
For most of the seven transition-metal impurities, calculations developed by researchers at Caltech and Yale University improved on the accuracy of conventional model-based predictions by as much as two orders of magnitude. The test involved the Kondo effect, a classic quantum problem whose general physics has been understood for decades even though its precise behavior in specific materials has remained difficult to calculate.
That gap between understanding the physics and predicting a real material is what the researchers set out to close. Rather than simplifying the electronic structure of the material before calculating its behavior, the team adapted highly accurate computational techniques originally developed in quantum chemistry to describe molecules.
“It is now possible to predict the properties of some complicated materials purely through computation without referring to experiment,” says Garnet Chan, Bren Professor of Chemistry, director of the Rudolph A. Marcus Center for Theoretical Chemistry at Caltech, and senior author of the study. “These first materials that we have studied are like a baby step, or a prototype problem, along the way to more complex phenomena such as high-temperature superconductors and quantum magnets.”
The work, led by Linqing Peng, PhD ’25, and Tianyu Zhu of Yale University, was published in Science. Both lead authors began working on the project in Chan’s laboratory at Caltech.
A simple effect exposes a hard problem
What makes the Kondo effect such a useful test is that the phenomenon is relatively simple to describe but much harder to predict quantitatively.
Place a single magnetic atom, such as iron or manganese, inside a metal such as copper and then cool the material. In an ordinary metal, electrical resistance steadily drops as the temperature falls, allowing current to flow more easily. With a magnetic impurity present, however, the trend eventually reverses. At a threshold known as the Kondo temperature, resistance reaches a minimum and then begins to rise.
“That is the signature of the Kondo effect, and it’s a property of the electrons in the impurity interacting with the electrons traveling through the bulk metal,” Chan explains.
Electron interactions reverse the resistance trend
The reversal is a visible consequence of a much more complicated interaction among electrons. The magnetic impurity contains unpaired electrons whose spin gives the atom its magnetism. At higher temperatures, the direction of this magnetic moment fluctuates freely.
As the metal cools, its electrons begin interacting more strongly with the impurity’s spin. They can flip their own spins in ways that partially cancel the magnetic moment of the embedded atom. Those interactions create additional scattering, producing the characteristic leveling off and eventual increase in electrical resistance.
At still lower temperatures, electrons throughout the surrounding metal collectively arrange themselves into a cloud that screens, or effectively cancels, the impurity’s magnetism.
This collective behavior makes the Kondo effect a classic many-body problem. In such systems, the behavior of many interacting particles cannot be understood simply by examining each particle independently. Physicists established the broad theory of the Kondo effect in the 1970s, with important contributions from Caltech alumnus Kenneth Wilson, PhD ’61.
The same challenge appears in more complicated strongly correlated materials. In familiar materials used in computing, including semiconductors such as silicon, interactions among electrons are weak enough that they often have little effect on overall behavior. In strongly correlated materials, the motion of one electron can depend sensitively on what many other electrons are doing.
That makes accurate calculations especially important for researchers trying to understand quantum materials such as high-temperature superconductors and quantum magnets.
Real materials push beyond simplified models
The Kondo effect became a benchmark for those efforts because researchers can state the underlying problem relatively simply and already understand its broad physics. What they have struggled to calculate is exactly how the resistance changes or precisely where the Kondo temperature falls for a particular impurity inside a particular real material.
Traditional computational approaches make the problem manageable by stripping away much of that real-material complexity. They typically reduce the electronic structure to a small number of orbitals, regions around an atom’s nucleus where electrons are most likely to be found, and then apply an approximate mathematical model.
Chan and his colleagues instead used computational tools from quantum chemistry to retain much more of the impurity’s actual electronic structure. Treating the magnetic atoms more like molecules allowed the researchers to calculate their interactions inside copper without relying on the same degree of simplification.
The seven transition-metal impurities provided a direct test of whether that more chemically faithful description could reproduce material-specific Kondo behavior. For most of the elements, it did so with substantially greater accuracy than the simplified model-based calculations.
A prototype for harder quantum materials
The systems tested so far are still far less complicated than the quantum materials researchers ultimately want to predict. But the results suggest that calculations incorporating the full chemical complexity of real materials are becoming practical for at least some strongly correlated systems.
“We are in an exciting era in which faithful predictive quantum descriptions of the full chemical complexity of real materials are coming within reach,” says Peng. “It is becoming realistic to predict material-specific behavior of correlated electrons from first principles, even in some of the most challenging classes of quantum materials.
“This is an important step toward computationally designing materials whose functions emerge from intricate correlated physics, such as high-temperature superconductivity, where the large chemical space and competition among many phases call for predictive theory to help focus the experimental search for new materials,” she adds. “I am excited to see what new materials breakthroughs this theory will enable in the future.”
Reference: “Toward an exact quantum many-body treatment of Kondo correlation in magnetic impurities” by Tianyu Zhu, Linqing Peng, Huanchen Zhai, Zhi-Hao Cui, Runze Chi and Garnet Kin-Lic Chan, 30 July 2026, Science.
DOI: 10.1126/science.adq7402
The work was supported by the Air Force Office of Scientific Research through the Multidisciplinary University Research Initiative program, the US Department of Energy and its Center for Molecular Magnetic Quantum Materials, and the US National Science Foundation
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