CTCP Seminar : “Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization” by Prof. Yidun WAN on Friday, Sept 20, 2024, 4:00 pm | CYMP 522

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.

“Representation Theory for Massless Quasiparticles in BdG Systems” by Prof Zheng-Xin LIU on Tuesday, July 2, 2024, 4:00 pm | CYMP 522

Linearly dispersive gapless quasiparticles can appear at general momentum points of superconductors due to topological reasons like K theory or symmetry indicators theory. However, the zero modes associated with these quasiparticles are generally ‘accidental’ from symmetry point of view. In this talk, we apply projective representation (rep) theory to analyze the bulk gapless quasiparticles in BdG systems. Different from the description of semimetals, we need to specially treat the particle-hole ‘symmetry’ since it is anti-comm-uting with the BdG Hamiltonian. Hence the notion of ‘simple irreducible reps (irreps)’ and ‘composite irreps’ are introduced to label the energy modes. We show that without charge conjugation symmetry (unitary symmetry that commutes with the Hamiltonian), no robust bulk zero modes exist at any fixed momentum point in the bulk. However, robust zero modes at certain high symmetry momentum points can be protected by (effective) charge conjugation symmetries, resulting in gapless quasiparticles with linear, quadratic, or higher-order dispersions determined by the effective k · p theory. The low energy physical properties of the system are determined by the rep carried by the zero modes. This theory provides a framework to classify nodal Superconductors/Superfluids/Quantum Spin Liquids with specified (projective) symmetry group and sheds light on the realization of Majorana-type massless quasiparticles in condensed matter physics.

Introduction to Superconductivity

This series of lectures are intended for interested undergraduate and graduate students. They
cover the fundamental aspects of classic superconductors and their explanations in terms of
the BCS theory of superconductivity.

HK Institute of Quantum Science & Technology
The University of Hong Kong
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