25 Years of Quantum Matter

“The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society. 

The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity, entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.”

— P.W. Anderson, “More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science,” August 4, 1972, Science, Vol 177, No. 4047

This classic quote by the late Philip Warren Anderson gets to the core of what the field of quantum matter is all about: The whole is more than the sum of its parts.

You cannot simply put a bunch of particles together and reconstruct the universe. In nature, everything is dynamic, and as you put particles together with other particles, new behaviours emerge that could not be found in the individual parts alone. This is a property of nature called emergence. 

Quantum matter physicists at Perimeter Institute’s Clay Riddell Centre for Quantum Matter are exploring all of the amazing possibilities that might come from these dynamical interactions.

“Quantum matter tries to understand phenomena that can arise from systems of many quantum degrees of freedom,” explains Timothy Hsieh, director of the Clay Riddell Centre for Quantum Matter.

Music (something that Hsieh knows well, as an accomplished violinist) provides an analogy. In a stringed instrument like a guitar or a violin, each string can vibrate in different patterns. These are comparable to degrees of freedom. But if the many degrees of freedom of many stringed instruments are vibrating together, you have something new: a symphony.

In quantum matter physics, it is as if many stringed instrument vibrations are arising and merging in a quantum symphony of possibilities.

The degrees of freedom could be in the electrons; it could be in the spin (a type of angular momentum in particles). It can be the magnetic moments (affecting the strength and direction of a magnetic field), or even, more recently, in the qubits in a quantum computer. “You can have hundreds, or thousands, or more, of quantum degrees of freedom interacting with each other,” Hsieh says. 

There are now more than 30 people associated with the Clay Riddell Centre for Quantum Matter, including faculty, associate faculty, postdoctoral researchers, and visiting researchers. 

This important development in Perimeter’s 25-year history was made possible by the Riddell Family Charitable Foundation. The Centre’s name honours Clay Riddell, an entrepreneur, and community builder who received the Order of Canada in 2008 for his leadership and philanthropy. 

Clay Riddell had a profound enthusiasm for scientific exploration and believed that investing in knowledge would make the world a better place. His partnership with Perimeter began in 2015 when he helped create the Clay Riddell Paul Dirac Chair in Theoretical Physics, held by faculty member Pedro Vieira. Prior to his passing in September 2018, he made the decision to partner with Perimeter to make the Clay Riddell Centre for Quantum Matter a reality. He viewed it as a high-impact investment for humanity. 

“Clay was incredibly excited to discover that we have a true gem like Perimeter Institute in Canada,” said Sue Riddell Rose when the research hub was launched. She is one of Clay’s four children, and President of the Riddell Family Charitable Foundation.

The funding for the Clay Riddell Centre for Quantum Matter has enabled Perimeter to attract new researchers to this important field – one that can play a major role in laying the foundations for future technologies.

Artificial quantum systems in quantum computers and quantum simulators is a new frontier of research that Hsieh and his colleagues are involved in.

In particular, the researchers are using them to explore what are known as “mixed state phases.” 

Mixed state phases in quantum computing can occur where there are long distance interactions between the qubits and the environment. This is known as noise or decoherence in a quantum system, and it is the bane of quantum computing today. It is at the heart of why it is difficult to build out a practical, fully functional quantum computer that can solve broad, real-world problems. The susceptibility to errors where there are large number of qubits hinders complex, large-scale computations. 

But noise can induce new phenomena and drive new classes of phase transitions, and this is what Hsieh, and his colleagues are studying. The study of these mixed state phases, defining them, and developing ways to recover the original state of the quantum system in the presence of noise would be key to creating better quantum error correction codes, which would help build a truly useful quantum computer. 

Perimeter faculty member Chong Wang says that in the everyday “classical” world, everyone is familiar with the simplest “phases of matter.” If you put water in an ice cube tray and put it in the freezer, it becomes ice. At room temperature it becomes water. Boil it on the stove and it becomes steam. Exposing a substance to different temperatures can cause it to take different forms. 

But when you start to study the quantum mechanical behaviours of particles, “there are many more possibilities,” Wang says.

What Wang finds most fascinating about quantum matter research is that we can even find answers to what happens when billions of particles are interacting with one another. “If we’re just thinking about the problem on its own, it would seem hopeless. And then quantum mechanics makes that complexity even worse,” he says.

But despite the seeming hopelessness, quantum matter researchers like Wang make progress by using mathematical tools to take the long view, contemplating the problem from a distance. 

“We ask about the properties that we see from the long distance, and typically at low energy, and low temperature. When we ask those questions, then it becomes simpler, and more elegant. Interesting patterns start to come out, emergent patterns that you couldn’t understand just from looking at the individual particles.”

An example of the cutting-edge quantum matter research done at Perimeter was a 2022 deep dive into what are known as “quantum spin liquids,” published in a paper in Physical Review X by Wang and his Perimeter colleagues Yin-Chen He and Liujun Zou. In it, they explored a theoretical form of quantum spin liquids called Stiefel liquids.

Quantum spin liquids are not actually liquid. However, the geometries of crystal lattices can sometimes make it difficult for electrons to line up in an orderly way, so they become “frustrated magnets” where the electrons are constantly fluctuating and interacting. Hence, they appear to have a liquid-like state. They are doing an entangled dance across the entire material, fluctuating around a “quantum critical” point – an in-between stage akin to the point of transition from one phase to another.

Quantum spin liquids were first proposed in 1973 by Nobel laureate Phil Anderson (whose quote we encountered above). At the time, they were purely theoretical, but since then, they have been created, and observed in laboratories. It is an example of the power of theoretical physics to create future material technologies.

Another quantum matter explorer at Perimeter, Dominic Else, received an Early Researcher Award from the Government of Ontario this year, to support his work on “non-Fermi liquids.” These are metals that have strong interactions between electrons, giving them some unusual properties, that conventional mathematical tools, and theoretical frameworks have not been able to fully explain. 

An example would be cuprates (compounds containing copper, often in a layered structure) that are interesting materials because they become superconducting at higher (although still quite cold) temperatures. 

These non-Fermi liquids are still poorly understood, and Else is working to identify, and test the general principles of metals that would apply to them. The project is also training two PhD students in in modern and innovative methods in condensed matter physics, thus growing Canada’s talent pool in this field.

When he was a postdoctoral researcher at Massachusetts Institute of Technology and Harvard University, Else gained recognition for his work on a headline-catching phase of matter known as “time crystals.”

If a crystal is a pattern that repeats in space, a time crystal is a pattern that repeats in time. Time crystals can oscillate between states periodically without external energy input, like a pendulum. If we could better understand them, they could have potential future applications in quantum computing, precision timekeeping, and long-lasting quantum sensors. Else won the prestigious New Horizons in Physics Prize in 2022 for this work. 

Researchers at Perimeter describe quantum matter physics as an act of exploration into new universes, and their vehicle for exploration, their spaceship, is mathematics.

“When we say that we explore them in a different universe, what we are saying is that for each material, there is some complicated mathematical description. But we can make it much simpler,” Wang says.

Although there is great technological promise in quantum matter, the researchers who study it are captivated by the unusual beauty of the collective behaviour of subatomic particles.

“When you put it all together, it’s not just a piece of music – you see a picture,” says Wang. “From time to time, something shockingly elegant, and beautiful emerges. I want to understand why.”