A complete classification could lead to a wealth of new materials and technologies. But some exotic phases continue to resist understanding.
Quanta Magazine said:In the last three decades, condensed matter physicists have discovered a wonderland of exotic new phases of matter: emergent, collective states of interacting particles that are nothing like the solids, liquids and gases of common experience.
The phases, some realized in the lab and others identified as theoretical possibilities, arise when matter is chilled almost to absolute-zero temperature, hundreds of degrees below the point at which water freezes into ice. In these frigid conditions, particles can interact in ways that cause them to shed all traces of their original identities. Experiments in the 1980s revealed that in some situations electrons split en masse into fractions of particles that make braidable trails through space-time; in other cases, they collectively whip up massless versions of themselves. A lattice of spinning atoms becomes a fluid of swirling loops or branching strings; crystals that began as insulators start conducting electricity over their surfaces. One phase that shocked experts when recognized as a mathematical possibility in 2011 features strange, particle-like “fractons” that lock together in fractal patterns.
Now, research groups at Microsoft and elsewhere are racing to encode quantum information in the braids and loops of some of these phases for the purpose of developing a quantum computer. Meanwhile, condensed matter theorists have recently made major strides in understanding the pattern behind the different collective behaviors that can arise, with the goal of enumerating and classifying all possible phases of matter. If a complete classification is achieved, it would not only account for all phases seen in nature so far, but also potentially point the way toward new materials and technologies.
Led by dozens of top theorists, with input from mathematicians, researchers have already classified a huge swath of phases that can arise in one or two spatial dimensions by relating them to topology: the math that describes invariant properties of shapes like the sphere and the torus. They’ve also begun to explore the wilderness of phases that can arise near absolute zero in 3-D matter.
“It’s not a particular law of physics” that these scientists seek, said Michael Zaletel, a condensed matter theorist at Princeton University. “It’s the space of all possibilities, which is a more beautiful or deeper idea in some ways.” Perhaps surprisingly, Zaletel said, the space of all consistent phases is itself a mathematical object that “has this incredibly rich structure that we think ends up, in 1-D and 2-D, in one-to-one correspondence with these beautiful topological structures.”
In the landscape of phases, there is “an economy of options,” said Ashvin Vishwanath of Harvard University. “It all seems comprehensible” — a stroke of luck that mystifies him. Enumerating phases of matter could have been “like stamp collecting,” Vishwanath said, “each a little different, and with no connection between the different stamps.” Instead, the classification of phases is “more like a periodic table. There are many elements, but they fall into categories and we can understand the categories.”
While classifying emergent particle behaviors might not seem fundamental, some experts, including Xiao-Gang Wen of the Massachusetts Institute of Technology, say the new rules of emergent phases show how the elementary particles themselves might arise from an underlying network of entangled bits of quantum information, which Wen calls the “qubit ocean.” For example, a phase called a “string-net liquid” that can emerge in a three-dimensional system of qubits has excitations that look like all the known elementary particles. “A real electron and a real photon are maybe just fluctuations of the string-net,” Wen said.
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