An Operator-Algebraic Framework for Anyons and Defects in Quantum Spin Systems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911362914975744 |
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| author | Vadnerkar, Siddharth |
| author_facet | Vadnerkar, Siddharth |
| contents | In this dissertation, we detail an operator algebraic approach to studying topological order in the infinite volume setting. We give a thorough and self-contained review of the DHR-style approach on quantum spin systems, which builds a category $\mathrm{\textbf{DHR}}$ of anyon sectors starting from microscopic lattice spin systems. In general, this category has the structure of a braided $\mathrm{C}^*$-tensor category. We will verify in full detail that $\mathrm{\textbf{DHR}}$ is the expected category in Kitaev's Quantum Double model, a paradigmatic model for studying topological order on the lattice. We will then extend the DHR-style analysis to systems in the presence of a global on-site symmetry, and introduce a category of symmetry defects, $G\mathsf{Sec}$, and show that it has the structure of a $G$-crossed braided $\mathrm{C}^*$-tensor category. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05515 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Operator-Algebraic Framework for Anyons and Defects in Quantum Spin Systems Vadnerkar, Siddharth Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Operator Algebras In this dissertation, we detail an operator algebraic approach to studying topological order in the infinite volume setting. We give a thorough and self-contained review of the DHR-style approach on quantum spin systems, which builds a category $\mathrm{\textbf{DHR}}$ of anyon sectors starting from microscopic lattice spin systems. In general, this category has the structure of a braided $\mathrm{C}^*$-tensor category. We will verify in full detail that $\mathrm{\textbf{DHR}}$ is the expected category in Kitaev's Quantum Double model, a paradigmatic model for studying topological order on the lattice. We will then extend the DHR-style analysis to systems in the presence of a global on-site symmetry, and introduce a category of symmetry defects, $G\mathsf{Sec}$, and show that it has the structure of a $G$-crossed braided $\mathrm{C}^*$-tensor category. |
| title | An Operator-Algebraic Framework for Anyons and Defects in Quantum Spin Systems |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Operator Algebras |
| url | https://arxiv.org/abs/2601.05515 |