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.

arXiv comment6 pages, 6 figures

References in corpus (26)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Spinor Bose-Einstein condensates
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Inversion Symmetric Topological Insulators
• The Zak phase and the existence of edge states in graphene
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Classifying Novel Phases of Spinor Atoms
• Synthetic Gauge Field with Highly Magnetic Lanthanide Atoms
• Entanglement and symmetry in permutation symmetric states
• Entanglement in the symmetric sector of $n$ qubits
• 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
• Barycentric measure of quantum entanglement
• N-qubit states as points on the Bloch sphere
• Searching for Non-Abelian Phases in the Bose-Einstein Condensate of Dysprosium
• Low energy dynamics of spinor condensates
• An alternative representation for pure symmetric states of qubits and its applications to entanglement classification
• Polynomial method to study the entanglement of pure N-qubit states

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• Delocalization of topological edge states
• Winding numbers of phase transition points for one-dimensional topological systems
• Extremal quantum states
• Anticoherence of spin states with point group symmetries
• Anticoherence measures for pure spin states
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices
• Quantumness Beyond Entanglement: The Case of Symmetric States
• Quantum Polarimetry
• Coherent-State Approach for Majorana representation
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Majorana stellar representation for mixed-spin $(s,\frac{1}{2})$ systems
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group