IQC Colloquium featuring Yidun Wan, Fudan University

Yidun Wan, Fudan University

Conformal field theories (CFTs) describe universal behaviour at continuous phase transitions and organize the entanglement of critical quantum systems. Microscopic lattice realizations make these theories accessible to numerical computation. Yet a systematic construction of critical lattice models with controlled symmetries has remained a decades-long challenge. Integrable models provide remarkable exact examples, but extending beyond these families requires a broader construction principle. 

In this colloquium, I will present our recent Nature Physics work on a “CFT factory” that derives local lattice weights and transition couplings from competing topological boundaries. The physical idea begins with different ways a topological phase can terminate, distinguished by which anyons its boundary can absorb. Competition between these boundary conditions generates critical lattice models. This gives a concrete holographic connection between topological order in 2+1 dimensions and critical physics in 1+1 dimensions. 

Using the toric code and Ising model as a running example, I will show how two familiar qubit states encode an exact critical coupling. I will then explain how tensor-network renormalization preserves the underlying symmetry while testing the resulting long-distance physics. The construction recovers established critical models and produces unfamiliar candidates, including models with Haagerup symmetry. These examples open opportunities for quantum-information methods to help identify new continuum theories. The emphasis will be on physical pictures and computational ideas, with no prior knowledge of conformal field theory or category theory assumed.