| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Boundary Hamiltonian Theory for Gapped Topological Orders |
| Yuting Hu1, Yidun Wan1,2, Yong-Shi Wu3,1,2,4** |
1Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433
2Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093
3State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433
4Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, 84112, USA
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| Cite this article: |
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Yuting Hu, Yidun Wan, Yong-Shi Wu 2017 Chin. Phys. Lett. 34 077103 |
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Abstract We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by (bi-) modules over Frobenius algebras.
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Received: 25 May 2017
Published: 06 June 2017
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| PACS: |
71.10.-w
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(Theories and models of many-electron systems)
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05.30.Pr
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(Fractional statistics systems)
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71.10.Hf
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(Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems)
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02.20.Uw
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(Quantum groups)
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