Representation of Berry phase by the trajectories of Majorana stars

Abstract

The Majorana's stellar representation, which represents the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, provides an intuitive way to study a physical system with high dimensional projective Hilbert space. In this Letter, we study the Berry phase by these stars and their loops on the Bloch sphere. It is shown that the Berry phase of a general spin state can be expressed by an elegant formula with the solid angles of Majorana star loops. Furthermore, these results can be naturally used to a general state with arbitrary dimensions. To demonstrate our theory, we study a two mode interacting boson system. Finally, the relation between stars' correlations and quantum entanglement is discussed.

12 pages, 2 figures

References in corpus (3)

• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase
• Searching for Non-Abelian Phases in the Bose-Einstein Condensate of Dysprosium

Cited by in corpus (13)

• Enhanced magnetic sensitivity with non-gaussian quantum fluctuations
• Characterization of symmetry-protected topological phases in polymerized models by trajectories of Majorana stars
• Anticoherence measures for pure spin states
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Link between \emph{Zitterbewegung} and topological phase transition
• Entangling power of symmetric two-qubit quantum gates
• The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
• Observation of nonlinear variations in three-vertex geometric phase in two-photon polarization qutrit
• Geometric decomposition of geodesics and null phase curves using Majorana star representation
• Berry phases of higher spins due to internal geometry of Majorana constellation and relation to quantum entanglement
• Robust quantum metrology with random Majorana constellations
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars