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A Return to the Fundamentals Approach Assists in Unravelling a New Phase of Matter

Computer modeling was used by researchers at the University of Cambridge to investigate potential new phases of matter known as prethermal discrete time crystals (DTCs). It was previously believed that the properties of prethermal DTCs were determined by quantum physics: the strange laws that govern subatomic particles. The researchers discovered, however, that a simpler approach based on classical physics can be used to explain these perplexing phenomena.

Understanding these new phases of matter is a significant step toward controlling complex many-body systems, a long-standing goal with numerous applications, including simulations of complex quantum networks. Two joint papers in Physical Review Letters and Physical Review B describe the findings.

When we discover something new, whether it's a planet, an animal, or a disease, we can learn a great deal about it by studying it more closely. Simpler hypotheses are tested first, and if they fail, more complicated hypotheses or methods are tried.

“This was our expectation for prethermal DTCs,” said Andrea Pizzi, a PhD student at Cambridge's Cavendish Laboratory and the first author on both papers. “We assumed they were fundamentally quantum phenomena, but it turns out that a more straightforward classical approach enabled us to gain a better understanding of them.”

DTCs are extremely complex physical systems, and much remains unknown about their peculiar properties. As with a standard space crystal, which violates space-translational symmetry because its structure varies throughout space, DTCs violate a distinct time-translational symmetry because their structure changes with each 'push'.

"Think of it as a parent pushing a child on a playground swing," Pizzi explained. "Typically, a parent pushes the child, the child swings back, and the parent pushes the child again. This is a relatively simple system in terms of physics. However, if that same playground had multiple swings and the children on them were holding hands, the system would become much more complex, and far more interesting and less obvious behaviors could emerge. A prethermal DTC is an example of this behavior, in which the atoms, acting like swings, only'return' every second or third push, for example."

DTCs were predicted in 2012 and have been studied in a variety of ways, including experiments. Prethermal DTCs are relatively simple-to-implement systems that do not heat rapidly as one might expect, but instead exhibit time-crystalline behavior for an extended period of time: the faster they are shaken, the longer they survive. However, it was previously believed that they were based on quantum phenomena.

“Developing quantum theories is difficult, and even if you succeed, your simulation capabilities are typically extremely limited, as the required computational power is enormous,” Pizzi explained.

Now, Pizzi and his co-authors have discovered that they can avoid overly complicated quantum approaches in favor of much more affordable classical ones for prethermal DTCs. This enables researchers to simulate these phenomena in a much more detailed manner. For example, they can now simulate a greater number of elementary constituents, gaining access to the most relevant experimental scenarios, such as two and three dimensions.

The researchers used classical Hamiltonian dynamics to study many interacting spins – like the children on the swings – under the action of a periodic magnetic field – like the parent pushing the swing. The resulting dynamics demonstrated the properties of prethermal DTCs succinctly and clearly: for an extended period of time, the system's magnetization oscillates with a period greater than that of the drive.

"It's remarkable how clean this method is," Pizzi said. "Because it enables us to examine larger systems, it makes it abundantly clear what is occurring. Unlike when we use quantum methods, we are not required to fight this system in order to study it. We hope that this research establishes classical Hamiltonian dynamics as a viable approach for large-scale simulations of complex many-body systems and opens new avenues for the study of nonequilibrium phenomena such as prethermal DTCs."

Dr. Andreas Nunnenkamp, now at the University of Vienna in Austria, and Dr Johannes Knolle, now at the Technical University of Munich in Germany, are Pizzi's co-authors on the two papers.

Meanwhile, Norman Yao's group at UC Berkeley in the United States of America has been studying prethermal DTCs using classical methods. Surprisingly, the Berkeley and Cambridge teams addressed the same question concurrently. Yao's group will soon publish their findings.

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