What’s New

An essential feature of topological crystalline states (TCSs), which are short-range-entanged topological states protected by crystalline symmetries, is they generally have high-order gapless boundary states, such as one-dimensional hinge states and zero-dimensional corner states on a two-dimensional surface. Therefore, such TCSs are also called high-order topological states. In this work, we design a systematic method to compute possible high-order boundary states of a TCS for all possible surface geometries. We show that the location of surface gapless region, dubbed the anomaly pattern, can be symmetrically and continuously deformed without changing the topologically-protected gapless states, and such deformation defines a homotopy equivalence between anomaly patterns. The list of equivalent classes of anomaly patterns are completely determined by the point-group symmetry, and it is universal for all types of TCSs, including bosonic, free-fermion and interacting-fermion states. We also describe how to compute the anomaly pattern of a bulk topological state, for all types of TCSs.

HK Institute of Quantum Science and Technology held its inaugural retreat on September 28, 2024, in Shenzhen. Following the signing of the Memorandum of Understanding (MOU), the delegation team engaged in discussions with the Quantum Science Center of the Guangdong-Hong Kong-Macao Greater Bay Area regarding potential future collaborations. Subsequently, the Institute conducted its first staff meeting chaired by Prof. Zidan Wang. During the retreat,  the team members visited two laboratories: Phase 1.5  Sun-Laboratory and  Phase2 Zhongtian-YuanLaboratory. To foster team spirit, we concluded the day with a team-building dinner.

We develop a systematic framework for understanding symmetries in topological phases in 2+1 dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon species and global symmetries permuting anyon species, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in 2+1 dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion 2-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input fusion categories that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input fusion categories, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models. If time permits, I will also talk about a subsequent work on anyon condensation.