Old Questions, New Frontiers: Solving Condensed-Matter Problems with Concepts from High-Energy Physics

Physicist Kun Chen studies the unexpected behavior of many interacting electrons in solids by developing methodologies originating in other areas of physics.

Quantum physicist Kun Chen.

When he was in graduate school, Kun Chen found himself gripped by a puzzling question: How could electrons, seemingly simple particles governed by straightforward equations of motion, lead to such complex and varied phenomena in everyday materials? Could these complexities be precisely predicted from basic physics? Driven by this profound question, he embarked on an academic journey to find answers.

More than six years into his exploration, Chen has discovered an especially effective way to describe the enigmatic behavior of electrons in materials. Drawing inspiration from recent advances in high-energy physics, he has developed a framework that holds promise for unraveling the complex collective behaviors seen in a range of materials from metals and semiconductors to superconductors.

A Research Fellow in the Flatiron Institute’s Center for Computational Quantum Physics (CCQ) from 2020 to 2023, Chen is now a researcher at the Chinese Academy of Sciences. He received a bachelor’s degree from the University of Science and Technology of China, a doctorate from the University of Massachusetts Amherst, and before joining CCQ was a Simons Postdoctoral Fellow at Rutgers University.

Chen recently spoke to the Simons Foundation about his work, and about the peculiarities of electrons. The conversation has been edited for length and clarity.

What is your current research focus?

In a nutshell, my research aims to borrow new insights and methodologies from high-energy physics to solve some fundamental problems in condensed-matter physics and material science. Effective field theory is a prominent example of this; it offers a very systematic way to model complicated problems with a minimal set of variables. I’ve found these techniques are very powerful in solving condensed-matter problems.

A significant challenge in condensed-matter physics is the many-electron problem. If you have a lot of electrons, they very strongly interact with each other. This means you can’t look at an individual electron; you have to understand their collective behavior. To give you a sense of scale, a 6-foot-long chunk of metal can have 1023 — that’s 100 sextillion — electrons. Their interactions govern the fundamental properties of various materials, ranging from metals and semiconductors to insulators. My research is focused on employing effective field theory to systematically model many-electron systems with unprecedented precision. The goal is not only to extend our theoretical tool kit but also to deepen our fundamental understanding of material behaviors.

How do you go about modeling these systems?

We’re taking an approach that I like to compare to one done by the artist Pablo Picasso. Picasso once did an artistic study where he kept drawing a bull, but simpler and simpler each time to find the most minimalist way to depict the animal. We’re doing the same with developing an effective field theory for electrons, but in reverse. First, we create the most basic model of the system and calculate its physical properties. Then, we compare this to a real system and see what we’re missing. We slowly add in more parameters until we reach a model that gives us a sufficiently accurate result. We’ve found that with only five parameters we can describe a simple metal with up to 90 percent accuracy. With more parameters, we can minimize the error to less than 1 percent.

Now we finally have a working model with unprecedented accuracy. We’re at the point where our model allows us to make precise predictions about collective electron behaviors, insights that have direct implications for materials and phenomena encountered in daily life.

What can these models help you understand about electron behavior?

I’m specifically using these models to dive deep into what I like to call the ‘puzzle of effective mass’ for electrons. Imagine a movie star walks through a room. Unlike an ordinary person, the movie star is well known, and people would crowd around them for signatures. As such, the movie star would have a harder time walking through the crowded room than an empty one — so you could say their ‘effective mass’ is larger when interacting with others. Similarly, you’d expect electrons interacting strongly with each other to have a different effective mass compared with a lone electron. Intriguingly, our calculations show that’s not the case; the two masses are nearly identical. So the big question is why, and we’re using our new model to figure that out. It is crucial not just as a fundamental puzzle but also for designing next-generation ab initio methods, which rely on fundamental principles and accurate approximations to predict material properties.

Now, this anomaly takes us to the concept of ‘naturalness,’ frequently discussed in high-energy physics. In essence, the naturalness principle suggests that any dimensionless numbers in physics should be near unity. In other words, the numbers should not be exceedingly large or vanishingly small. For instance, the gravitational constant — the number describing ­­­­how strongly masses are attracted —is far smaller than unity, which has puzzled scientists for ages. Similarly, in the realm of electronic structure, we’d expect electrons’ effective mass to change notably due to strong interactions, in line with this principle of naturalness. Yet surprisingly, it doesn’t. This gives us a ‘naturalness problem’ right within the electronic structure theory. The fascinating aspect is that connecting these two seemingly separate problems could give us new insights into both fields.

Will other scientists be able to use the models and tools you’ve created?

Effective field theory is an incredibly powerful approach, often considered a cornerstone in high-energy physics for its ability to systematically simplify complex systems. But when it comes to using it in condensed-matter physics, there have been some technical roadblocks. That’s what got us thinking: What if we could make this more approachable? So we came up with Numerical Effective Field Theory, or NEFT for short. We just showcased it at a conference, and it’s already available on GitHub for anyone to use. We’re thrilled, because we think this tool kit will open doors. It makes the brilliance of effective field theory accessible to more condensed-matter physicists and material scientists, and we’re really excited to see where it takes us.