Physicists worked out the general theory in the 1970s, with Caltech alumnus Kenneth Wilson (PhD '61) among the key contributors. The problem became a classic many-body challenge: it demands describing a huge number of interacting particles whose behavior cannot be reduced to treating electrons one at a time. That is also why it became a benchmark for testing new computational techniques.

Why did old methods fall short?

In ordinary semiconductors like silicon, electrons interact weakly enough that researchers can ignore those interactions when modeling a material's overall behavior. Strongly correlated materials — important for many proposed quantum technologies — do not allow that shortcut. There, how each electron scatters off its neighbors is essential to the physics.

Traditional approaches simplified a material's electronic structure into a small set of orbitals — the regions around an atom's nucleus where electrons most likely reside — and then applied an approximate mathematical model to that smaller system. The simplification lost chemical detail, and with it accuracy.

Chan's group took a different route. They adapted highly accurate computational tools originally built in quantum chemistry for describing molecules and applied them to quantum materials. The approach let them treat magnetic impurities almost as if they were molecules while keeping the full complexity of their electronic interactions.

What did the calculations show?

The team tested the method on seven different transition-metal atoms embedded in copper. For most of those elements, the results were as much as two orders of magnitude — a factor of up to 100 — more accurate than predictions from conventional model-based techniques.

Lead authors Linqing Peng (PhD '25) and Tianyu Zhu of Yale began the project in Chan's laboratory at Caltech, home of the Rudolph A. Marcus Center for Theoretical Chemistry. Additional Caltech authors are Huanchen Zhai, Runze Chi, and Zhi-Hao Cui (PhD '23).

"We are in an exciting era in which faithful predictive quantum descriptions of the full chemical complexity of real materials are coming within reach," Peng says.

She adds that the work is "an important step toward computationally designing materials whose functions emerge from intricate correlated physics, such as high-temperature superconductivity," where predictive theory can help focus experimental searches across a vast chemical space.

How far does the result reach?

The researchers frame their achievement carefully. The materials studied here are a starting point, not the finish line.

"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," Chan says.

High-temperature superconductors remain harder because every electron's behavior depends strongly on what neighboring electrons do, defying the approximations conventional simulations rely on. If the new approach scales, realistic computer simulations of such systems move from aspiration to design tool.

The research drew support from 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.

A prototype problem is now exactly solvable — and that opens a tested path toward the harder ones.