2024/12/27 by Zhian Jia, Jia, Zhian · 4 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2412.19657
openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We propose a (1+1)D lattice model, inspired by a weak Hopf algebra generalization of the cluster state model, which realizes Haagerup fusion category symmetry and features a tensor product Hilbert space. The construction begins with a reconstruction of the Haagerup weak Hopf algebra H3 from the Haagerup fusion category, ensuring that the representation category of H3 is equivalent to Haagerup fusion category. Utilizing the framework of symmetry topological field theory (SymTFT), we develop an ultra-thin weak Hopf quantum double model, characterized by a smooth topological boundary condition. We show that this model supports Haagerup fusion category symmetry. Finally, we solve the ground state of the model in terms of a weak Hopf matrix product state, which serves as a natural generalization of the cluster state, embodying Haagerup fusion category symmetry.