Boundary Hamiltonian theory for gapped topological phases on an open surface

DOI10.1007/JHEP01(2018)134zbMath1384.81126arXiv1706.03329OpenAlexW2626479459MaRDI QIDQ1745549

Yidun Wan, Yong-Shi Wu, Yuting Hu, Zhu-Xi Luo, Ren Pankovich

Publication date: 17 April 2018

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03329

zbMATH Keywords

topological field theoriesquantum groupstopological states of matter

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Topological field theories in quantum mechanics (81T45)

Related Items (14)

Gapped boundary theory of the twisted gauge theory model of three-dimensional topological orders ⋮ Entanglement entropy of topological orders with boundaries ⋮ Boundary and domain wall theories of 2d generalized quantum double model ⋮ Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries ⋮ Ishibashi states, topological orders with boundaries and topological entanglement entropy. I ⋮ Anyonic exclusions statistics on surfaces with gapped boundaries ⋮ Gapped interfaces in Fracton models and foliated fields ⋮ The boundary phase transitions of the 2+1D \(\mathbb{Z}_N\) topological order via topological Wick rotation ⋮ From effective Hamiltonian to anomaly inflow in topological orders with boundaries ⋮ Ishibashi states, topological orders with boundaries and topological entanglement entropy. II: Cutting through the boundary ⋮ Entanglement entropy, quantum fluctuations, and thermal entropy in topological phases ⋮ Boundary topological entanglement entropy in two and three dimensions ⋮ One dimensional gapped quantum phases and enriched fusion categories ⋮ Extend the Levin-Wen model to two-dimensional topological orders with gapped boundary junctions

Cites Work

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• Models for gapped boundaries and domain walls
• Fermionic quantum computation
• The quantum double model with boundary: condensations and symmetries
• Anyon condensation and tensor categories
• Module categories, weak Hopf algebras and modular invariants
• Fault-tolerant quantum computation by anyons
• Generalized ADE classification of topological boundaries and anyon condensation
• Non-Abelian anyons and topological quantum computation
• Topological quantum computation with gapped boundaries and boundary defects
• Topological quantum computation
• Topological quantum memory
• Quantum statistics and superconductivity in two spatial dimensions

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