ASU researcher Yang Jiao discovers special state of matter

Yang Jiao, a professor in the School for Engineering of Matter, Transport and Energy, part of the Ira A. Fulton Schools of Engineering at Arizona State University, demonstrates his work mathematically in his office. He discovered the existence of hyperuniformity, an exotic state of matter, in quantum mechanical systems. Photographer: Erika Gronek/ASU

The ancient Chinese concept of yin and yang — which describes how seemingly opposite forces such as day and night are interconnected and interdependent — can be used to understand the concept of hyperuniformity. Yang Jiao, a professor of materials science and engineering in the School for Engineering of Matter, Transport and Energy, part of Ira A. Fulton Schools of Engineering at Arizona State University, studies the new material state. Just as dusk is the time of day when light gradually fades into darkness while the distinct qualities of the two coexist, hyperuniform material systems exhibit properties of both crystal solids and liquids simultaneously, creating a unique state of matter.

“Hyperuniformity is a defining property, just like rigidity is what makes something a solid material,” Jiao says. “In that sense, material systems with a distinct mix of being ordered and disordered at the same time are said to be in a hyperuniform state.”

Hyperuniformity isn’t a new material state. In fact, it has been extensively studied in classical materials systems since its discovery by Princeton University researchers Salvatore Torquato and Frank Stillinger in their 2003 paper “Local density fluctuations, hyperuniformity, and order metrics.” However, there’s been much less exploration of the property in quantum systems — think atoms, electrons, or tiny particles that follow rules different from the classical physics of everyday life.

Through the Multidisciplinary University Research Initiative, a program funded by the U.S. Department of Defense, a group of researchers that includes Jiao demonstrated for the first time the existence of hyperuniformity in quantum spin liquids, a type of quantum system classically known to be disordered. Jiao’s collaborators include Torquato; Duyu Chen, a postdoctoral researcher at the University of California, Santa Barbara; and Rhine Samajdar, a postdoctoral researcher at Princeton University. Their work has been published in the Proceedings of the National Academy of Sciences, a peer-reviewed journal published by the National Academy of Sciences.

“I believe the spin liquid is the first example of a strongly correlated, long-range entangled quantum mechanical system identified to have hyperuniform behavior,” Jiao says. “Usually, people classify any system that is locally disordered as liquid or glass. We found that it’s much more interesting.”

Jiao’s work deals with material structures at an atomic level. Every neutral atom is made of a nucleus with a specific number of protons and an equal number of electrons. One can equate a material’s atomic structure to a pizza. Its center, where all the slices lead, would be like the nucleus in which protons exist, and the toppings spread across the pizza represent electrons floating around the nucleus.

“Using two-dimensional systems as an example, moving electrons causes electrical current, which creates a magnetic field,” Jiao says. “At a quantum level, electrons have a spin, which can be thought of as a tiny magnet influencing their interactions and behavior in a material system.”

Just like how toppings on a pizza can be rotated clockwise or counterclockwise, electron spins can face either down or up, and one spin’s orientation affects how neighboring spins behave.

Discovering new laws of nature

“In solid materials, atoms arrange themselves in a very ordered way,” Jiao says. “For the liquids, atoms are packed densely, but it’s disordered, so they can slide around each other. In gases, atoms are scattered around with very high kinetic energy.”

Jiao worked with a quantum mechanics expert to develop advanced algorithms that simulate materials’ properties at an atomic level. Then, using a technique called density fluctuations analysis, which is used in physics to identify variations in how many particles or atoms are in a given space, the research team studied the fundamental structures of materials in various states. Looking through differently sized virtual windows into a material system, they counted atoms seen through each window.

Jiao says that in regular disordered material systems like liquids, the fluctuations in the number of atoms grew quickly with the window size — specifically, the area inside of the window in a two-dimensional system. On the other hand, in crystals, where all the atoms are ordered, the fluctuations grew with the window’s perimeter because only the boundary contributes to variation, not the change in the number of atoms inside the window.

“Hyperuniformity in quantum mechanical systems is a new and exotic state, which is kind of a hard knock on our traditional wisdom of how atoms can arrange themselves to make a material,” Jiao says. “Up close, they look disordered like a liquid, but when you look at their density fluctuations through bigger and bigger windows, they grow slowly like a crystal would, proportional to the perimeter rather than the area.”

Despite successfully identifying hyperuniformity in quantum spin liquids, Jiao and the team faced a big challenge.

“Typically, when people do these quantum mechanical simulations, they look at a very small-scale system,” Jiao says. “But because hyperuniformity can only be observed on a large scale, we had to simulate the largest quantum spin liquid system ever.”

Accelerating materials discovery using artificial intelligence

Beyond contributing to the scientific understanding of material structures and states of matter, Jiao foresees hyperuniformity in quantum systems leading to innovations in various fields.

“Hyperuniformity could become an important foundation for quantum computing,” Jiao says. “Quantum computing isn’t my area of expertise, but because regular computers use binary code made of zeroes and ones, the hyperuniformity in quantum spin liquids — disorder on a small scale with random spin directions, but order on a large scale with aligned spins — could provide a feasible way to build stable quantum computing technology, which operates outside of traditional binary code rules.”

While the team relied heavily on physics-based simulations to make progress on the project, Jiao says that generative artificial intelligence models present an exciting opportunity to easily simulate larger quantum mechanical systems.

“Using AI tools can make future research in this area much more effective,” he says.

Jiao plans to capitalize on the momentum and dig a bit deeper into the fundamental rules that govern hyperuniform systems.

“Hyperuniformity is a really interesting state, not only because it combines order and disorder, but because it corresponds to optimal system properties that can’t be achieved in other states,” he says. “One of the major things I want to push for is to discover the underlying mechanisms and use hyperuniformity to engineer novel material systems.”