A team of theoretical researchers have found duality can unveil non-invertible symmetry protected topological phases, which can lead to researchers understanding more about the properties of these phases, and uncover new quantum phases. Their study was published in Physical Review Letters on January 30.

Symmetry is one of the most fundamental concepts for understanding phases of matter in modern physics. In particular, “Symmetry-Protected Topological (SPT) phases,” whose quantum mechanical properties are protected by symmetries, with possible applications in quantum computing and other fields.

Over the past few years, “non-invertible symmetries,” which extend the framework of conventional symmetries, have attracted significant attention in high energy physics and condensed matter physics. However, their complex mathematical structures have made it difficult to understand their corresponding phases of matter, or Symmetry-Protected Topological (SPT) phases.

In this study, a research group led by University of Southern Denmark Researcher Weiguang Cao, The University of Tokyo Department of Physics and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI) Professor Masahito Yamazaki, and Ghent University Researcher Linhao Li (currently at Pennsylvania State University), successfully established a classification and construction method for topological phases protected by “non-invertible symmetries”, or SPT phases, by using a method known as “duality.”

Duality refers to a mathematical equivalence between seemingly different physical systems. By using duality transformations, this complex problem could be reduced to a better-known physical phenomenon called “phases with spontaneously broken conventional symmetries (SSB phases)” (Figure 1). This enabled researchers to classify SPT phases with non-invertible symmetries in arbitrary dimensions, and the successful construction of concrete models.
The models constructed in this study offer important theoretical insights for applications in quantum technology, such as future quantum simulations and the design of quantum devices utilizing topological properties.