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Symmetry topological field theory (SymTFT), also known as topological holography, posits a correspondence between symmetries in a d dimension theory and topological order in (d+1)-dimension. In this talk, I will present lattice realizations of SymTFT within the framework of quantum group symmetries. I will explain how to reconstruct a weak Hopf symmetry from a given topological order, and how boundary–bulk duality can be characterized in terms of quantum group symmetry. I will then present an explicit lattice construction of generalized cluster state models exhibiting non-invertible symmetries, along with a discussion of their possible generalizations.
Biography: Zhian Jia is a specially appointed Associate Professor in the School of Physics at Central South University. He received his PhD from the University of Science and Technology of China. He has also been a visiting scholar at Tsinghua University and the University of California, Santa Barbara. After graduation, he worked as a Research Fellow at the Centre for Quantum Technologies, National University of Singapore, for several years before returning to Central South University in 2026, where he currently holds his position. His research interests include mathematical physics, topological order, generalized symmetries in quantum field theory and lattice models, as well as quantum information and quantum computation theory.
Prof. Yinan Wang