Abstract
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a ()-dimensional Hilbert space (or, equivalently, of a spin- system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.
- Received 10 April 2012
DOI:https://doi.org/10.1103/PhysRevLett.108.240402
© 2012 American Physical Society
Viewpoint
A Quantum Constellation
Published 11 June 2012
Majorana’s geometrical representation of quantum spin as points on a sphere offers an intuitive approach to understanding quantum systems with multiple components.
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