Thursday, April 12, 2012

1204.2372 (Patrick Bruno)

Geometric phase of spin systems in Majorana's stellar representation: a
fictitious many-body Aharonov-Bohm effect
   [PDF]

Patrick Bruno
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of spin systems is studied. It is shown that the quantum state of a spin J can be mapped onto the partition function of a fictitious gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J 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.
View original: http://arxiv.org/abs/1204.2372

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