Physicists Develop New Tool for Identifying Phases of Matter

New Tool for Identifying Phases of Matter


Even if you’re not a physicist, phases of matter … really matter. They’re the distinct physical forms taken on by all the “stuff” in the universe, from icebergs to ozone, and now Yale scientists have developed a more accurate way to help classify some of them.

The findings appear in a recent study published in the journal Physical Review Letters and a follow-up work published in Physical Review B.

The fundamental phases of matter — solid, liquid, and gas — are well known. But there are many other phases, including ones that emerge when matter is chilled or heated to extreme temperatures. Extreme heat, for example, can create plasma phases by breaking down the individual atoms in a substance. Extreme cold, on the other hand, down to nearly absolute zero, triggers an array of quantum phases in which particles interact in entirely new ways.

Understanding the intricacies of these phases could unlock breakthroughs in quantum computing and materials science. In fact, some of these phases could be used as quantum hard drives that will store quantum information. That’s why scientists are actively seeking new approaches to characterize and classify them.

More than a decade ago, Caltech physicists Alexei Kitaev and John Preskill and concurrently Michael Levin along with Xiao-Gang Wen at MIT pioneered a new diagnostic tool — called topological entanglement entropy — for identifying whether a phase of matter is topological. Topology explains why you can turn a doughnut shape into a coffee cup shape by simply deforming its surface. Topologically speaking, a coffee cup is the same as a doughnut because they both have one hole.

Topology is particularly important in quantum research because the robust properties of topological phases establish a measure of stability within the highly delicate, and unpredictable, world of quantum physics. Similar to the doughnut example in which the number of holes doesn’t change under smooth deformations, topology appears in the patterns of quantum entanglement in a topological phase. The principle of topological entanglement entropy can detect such patterns.

A team of Yale researchers led by physicist Meng Cheng found a discrepancy in the principle that could lead to a false result. The team included graduate student Arpit Dua and postdoctoral associate Dominic Williamson.

“Because of its fundamental nature, this principle has been used extensively in the literature on topological phases,” Dua said.

The culprit, Dua said, is a specific kind of hidden string order that crops up in parts of the phase of matter. The researchers’ first study points out the discrepancy, explains why it occurs, and offers a way to correct for the error — thus making the principle more accurate. In the second study, the researchers look at an important class of phases where the discrepancy occurs, phases that could be used for making quantum hard drives. The researchers discuss a quantity that can be used to classify these phases, a quantity that is robust to the presence of the hidden string order that affects topological entanglement entropy.

“Topological phases represent an important class of phases of matter,” Dua said. “Their study and methods for diagnostics are important, and identifying the right diagnostic tools is fundamental.”


  • “Spurious Topological Entanglement Entropy from Subsystem Symmetries” by Dominic J. Williamson, Arpit Dua and Meng Cheng, 12 April 2019, Physical Review Letters.
    DOI: 10.1103/PhysRevLett.122.140506
  • “Compactifying fracton stabilizer models” by Arpit Dua, Dominic J. Williamson, Jeongwan Haah and Meng Cheng, 19 June 2019, Physical Review B.
    DOI: 10.1103/PhysRevB.99.245135

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