Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars

Abstract

By using Majorana's stellar representation, we give a clear geometrical interpretation of the topological phases of inversion-symmetric polymerized models by mapping the Bloch states of multi-band systems to Majorana stars on the Bloch sphere. While trajectories of Majorana stars of a filled Bloch band exhibit quite different geometrical structures for topologically trivial and nontrivial phases, we further demonstrate that these structures are uniquely determined by distributions of Majorana stars of two high-symmetrical momentum states, which have different parities for topologically different states.

6 pages, 6 figures

References in corpus (7)

• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Classifying Novel Phases of Spinor Atoms
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase
• Classifying Vortices in S=3 Bose-Einstein Condensates
• Representation of Berry phase by the trajectories of Majorana stars
• Searching for Non-Abelian Phases in the Bose-Einstein Condensate of Dysprosium

Cited by in corpus (9)

• Delocalization of topological edge states
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• Anticoherence measures for pure spin states
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• Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Quantum Polarimetry
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group