Frustration-Free Models for Topological Holography: Fusion Spin Chains as Boundary Algebras

arXiv:2609.28120 · math-ph, cond-mat.str-el, math.MP, math.OA, quant-ph · Submitted 2026-09-23 · Read on arXiv

math-ph, cond-mat.str-el, math.MP, math.OA, quant-ph

Submitted: 2026-09-23

Updated: 2026-09-23

Comments: 32 pages, 5 figures. Comments welcome!

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Frustration — 28× in this paper · explained in 2 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Topological Order — 7× in this paper · explained in 2 episodes
• Trace — 7× in this paper · explained in 2 episodes
• Entanglement — 3× in this paper · explained in 3 episodes
• Anyons — 2× in this paper · explained in 2 episodes
• Axioms — 2× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Modular flow — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Topological Defects — 1× in this paper · explained in 2 episodes

Sources

• Topological Defects on the Lattice: Dualities and Degeneracies
• Boundary algebras of the Kitaev Quantum Double model
• An operator algebraic approach to fusion category symmetry on the lattice
• Interacting anyons in topological quantum liquids: The golden chain
• Solving Gapped Hamiltonians Locally
• Reflection Positivity and Levin-Wen Models
• Holography for bulk-boundary local topological order
• Local topological order and boundary algebras
• DHR bimodules of quasi-local algebras and symmetric quantum cellular automata
• Non-invertible anomalies and mapping-class-group transformation of anomalous partition functions
• Fault-tolerant quantum computation by anyons
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Boundary-bulk relation in topological orders
• Generalized Kramers-Wannier Self-Duality in Hopf-Ising Models
• Dualities in one-dimensional quantum lattice models: topological sectors
• An entropic characterization of Haag duality
• String-net condensation: A physical mechanism for topological phases
• Topological Orders from Reflection Positive Frustration-free Hamiltonians
• Stability of Frustration-Free Hamiltonians
• Local topological order, Haag duality, and reflection positivity

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