Topological Phases
Topological phases of matter highlights the deep interplay of symmetry and topology and is stable under various local perturbations.
We study the entanglement scaling of 2+1 dimensional critical systems. Our main results include:
We developed a systematic approach to study the topological phases through analyzing the boundary gapless theory. Our main results include:
- The boundary gapless theory exhibits quantum anomaly if the bulk topological phase is protected by symmetry.
- By defining the appropriate boundary theory, we establish the bulk-boundary correspondence in a large class of 3+1 dimensional bosonic topological phases. We further analyze the possible braiding statistics of bulk topological excitations.
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We introduce the twist defect in 2+1 dimensional topological phases and systematically study fusion and braiding statistics for it. This method can also help us construct more exotic non-abelian topological phases by introducing and proliferating symmetry defects in the parent topological phases.
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We use the twist defect to construct a series of 1+1 dimensional spin chain model and analyze the critical point described by the orbifold CFT.
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We establish the connection between gauging symmetry in bulk topological phase and orbifolding symmetry in boundary gapless phase in 3+1 dimensions.
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