Two studies on critical topology have recently been published in the internationally renowned journal Nature. These studies were led by the teams of Prof. Baile Zhang at Nanyang Technological University, Singapore, and Prof. Jianhua Jiang at the University of Science and Technology of China, respectively. Prof. Xue-Jia Yu from the School of Physics at the Eastern Institute of Technology, Ningbo (EIT), served as a co-corresponding author on both papers and provided key theoretical guidance in the related experimental collaborations.
Topology: A Robust Framework Protected by Topological Invariants
To understand the significance of this work, we first need to discuss the concept of topology.
In the conventional picture of physics, the states of matter are determined by symmetry. For example, the transition of water into ice and the magnetization of iron are both results of symmetry breaking. However, the discovery of topological phases of matter fundamentally changed this understanding (recognized by the 2016 Nobel Prize in Physics). Topology focuses on global properties of objects that remain unchanged under continuous deformation. As an analogy, a coffee mug and a doughnut are considered equivalent from the perspective of topology: the handle of the mug can be continuously deformed into a hole, and as long as the object is not torn or glued, the number of holes remains unchanged.
This quantized robustness gives topological phases of matter a natural advantage: exceptional stability. The quantum Hall effect, topological insulators, and other representative topological materials rely on the protection of global topological invariants. Even in the presence of symmetry-preserving impurities and perturbations, their conducting edge states remain robust. However, this protection has a prerequisite—the bulk state of the material must possess an energy gap. Once the energy gap closes, the topological invariant is no longer well defined, and the edge states disappear accordingly. Therefore, the scientific community has long held the principle that topological phases of matter are inherently associated with the existence of an energy gap.
Criticality: Where Distinct Systems Exhibit Universal Behavior
In contrast to the "rigidity" of topology is the critical point in continuous phase transitions—for example, the transition of water into vapor at the boiling point and the loss of magnetism at the Curie point. Near a critical point, the energy gap of a system completely closes, microscopic details are smoothed out, and only collective behaviors at long wavelengths remain. At this point, materials with very different microscopic properties can exhibit exactly the same critical exponents and belong to the same universality class. This is one of the most fascinating discoveries in physics (recognized by the 1982 Nobel Prize in Physics): at critical points, seemingly diverse systems can converge into the same universal description.
However, this framework appears almost entirely incompatible with topological phases of matter. Critical points are gapless, whereas topology requires an energy gap; criticality is continuous, whereas topology is characterized by discrete invariants. For decades, these two fundamental pillars of physics were regarded as two separate domains that developed independently with limited overlap.
From a Long-Standing Boundary to a New Frontier: Years of Theoretical Exploration by Xue-Jia Yu's Team
"Can topology survive at a critical point?" This question was once considered a fundamental challenge to the conventional understanding of topology in physics. In recent years, a small number of theoretical physicists, including Prof. Xue-Jia Yu, have begun to systematically explore this possibility. Prof. Yu and collaborators have carried out a series of theoretical studies in this direction. In 2022, they proposed a theoretical classification theory for topology at quantum critical points [PRL 129, 210601]; In 2024, they proposed a generalized topological bulk–edge correspondence applicable to critical points [PRL 133, 026601]; In 2026, they further extended the related theory to nonequilibrium dynamics [PRL 137, 096605 (Editor's Suggestions)]. In addition, Prof. Xue-Jia Yu collaborated with Prof. Limei Xu from Peking University and Chair Professor Hai-Qing Lin from Zhejiang University. Together, they were invited to publish the first comprehensive review article on this topic in the internationally recognized journal Physics Reports [Physics Reports 1160, 1-56 (2026)]. This review article systematically summarizes the complete theoretical framework of critical topology.
The Theory Was Ready, but Experimental Realization Remained Difficult
Although the theoretical framework had gradually become clearer, experimental realization had remained challenging. To realize critical topology in a real physical system, researchers need to precisely tune the system to a critical point, where the bulk state becomes completely gapless. At the same time, they must detect the signatures of topological edge states against strong fluctuations and background noise. This challenge is extremely demanding: it is almost like stopping a high-speed train precisely at the edge of a cliff while still measuring a tiny particle of dust on the wheel. Therefore, for many years, the exciting predictions of critical topology remained only in theoretical studies and numerical simulations.
Theoretical Contributions from EIT Underlie Two Independent Experiment
This situation has now been changed. Prof. Xue-Jia Yu collaborated with the experimental teams of Prof. Baile Zhang from Nanyang Technological University, Singapore, and Prof. Jianhua Jiang from the University of Science and Technology of China. Using acoustic metamaterials as an artificial platform, the teams experimentally observed critical topological phenomena and achieved a breakthrough from theoretical prediction to experimental realization. The two experiments adopted completely different design strategies and measurement approaches. As a co-corresponding author of both Nature papers, Prof. Yu provided key support in theoretical modeling, mechanism interpretation, and analysis of the physical picture related to the experiments.
In the first study ("Observation of critical topological phase transition"), Based on the theoretical framework proposed by Prof. Xue-Jia Yu and further developed together with collaborators (Communications Physics 8, 1 (2025)), the experimental team successfully observed topological zero-energy modes and π modes at a one-dimensional Floquet critical point, experimentally realizing the critical topological phenomena. The co-first authors of this work are Dr. Zheyu Cheng, Postdoctoral Fellow at Nanyang Technological University, and Dr. Xiuhai Zhang, Postdoctoral Fellow at Northwestern Polytechnical University. The co-corresponding authors are Prof. Xue-Jia Yu, Prof. Longwen Zhou from Ocean University of China, Prof. Jiangbin Gong from National University of Singapore, and Prof. Baile Zhang from Nanyang Technological University.
In the second study ("Experimental observation of critical topology"), the experimental team adopted the generalized Li–Haldane bulk–edge correspondence proposed by Prof. Xue-Jia Yu [PRB 112, 075129 (2025); PRR 8, 023203 (2026)]. Through experimental measurements of the entanglement spectrum, the team achieved the observation of one-dimensional and two-dimensional critical topological phenomena. The co-first authors of this work are Dr. Zhikang Lin, Postdoctoral Fellow at The University of Hong Kong; Mr. Liwei Wang, Ph.D. student at the University of Science and Technology of China; and Dr. Zelín Kong, Postdoctoral Fellow at Soochow University. The co-corresponding authors are Prof. Xue-Jia Yu, Prof. Shuang Zhang from The University of Hong Kong, and Prof. Jianhua Jiang from the University of Science and Technology of China. Other collaborators include Dr. Yao Zhou, Postdoctoral Fellow at The University of Hong Kong, and Chair Professor Hai-Qing Lin from Zhejiang University.
Two papers, two independent experiments, and the same theoretical origin—the team of Prof. Xue-Jia Yu at EIT, served as the core theoretical support underlying both studies.
From "Impossible" to Experimental Realization
These two independent Nature studies provide the first experimental evidence in real physical systems that: topology can survive even when the energy gap closes; critical universal behavior and topological properties can coexist. These findings not only transform critical topology from a theoretical concept into experimental reality, but also open new possibilities for future studies of topological quantum computation, novel acoustic devices, and nonequilibrium topological phases of matter.
Topology and criticality, two concepts once considered incompatible, have finally met in the laboratory. The main theoretical force behind this convergence came from Prof. Xue-Jia Yu's team at the Eastern Institute of Technology, Ningbo.
About Xue-Jia Yu's Research Group
The research group led by Prof. Xue-Jia Yu primarily focuses on theoretical and computational studies of quantum phase transitions and critical phenomena in strongly correlated many-body systems, within the broader contexts of statistical physics and condensed matter physics. Their work integrates analytical approaches with large-scale numerical simulations, employing a diverse toolkit that includes quantum (conformal) field theory, tensor networks, and quantum Monte Carlo algorithms. Over the years, they have produced a series of innovative achievements in quantum phase transition and critical theory, non-equilibrium quantum criticality, and quantum simulation. In particular, the group has been at the forefront of the emerging field of topological physics at quantum critical points. As one of the early contributors to this direction, they have, over the past five years, consistently generated highly influential research results as primary corresponding authors, including two papers in Nature. Their expertise has been recognized by an invitation to write the first comprehensive review article in this area. Representative works include the systematic construction of a theoretical framework for topological invariants at quantum critical points and the elucidation of the corresponding topological bulk–edge correspondence.
Currently, the group is recruiting postdoctoral researchers and Ph.D. students. They warmly welcome young talents to join.
