Geometric phases and criticality in spin chain systems

Angelo C. M. Carollo, Jiannis K. Pachos

Published 2005-02-11, updated 2005-08-04Version 2

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that correspond to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. Ultra-cold atoms in optical lattices are presented as a possible physical realization.