Commuting-projector Hamiltonians for chiral topological phases built from parafermions
| Autor: | Son, Jun Ho, Alicea, Jason |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 97, 245144 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.97.245144 |
| Popis: | We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve $\mathbb{Z}_{3}$ parafermion zero modes residing in a parent fractional-quantum-Hall fluid. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which $\mathbb{Z}_2$ spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced $\mathbb{Z}_3$ parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with $\text{SU}(2)_{4}$ topological order, and can be accessed by gauging the $\mathbb{Z}_{2}$ symmetry in the SET. Employing Levin-Wen string-net models with $\mathbb{Z}_{2}$-graded structure, we generalize this picture to construct a large class of commuting-projector models for $\mathbb{Z}_{2}$ SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order. Comment: 29+18 pages, 25 figures |
| Databáze: | arXiv |
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