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Geometric phases and criticality in spin chain systems

Angelo C. M. Carollo·Jiannis K. Pachos
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Abstract

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.

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Angelo C. M. Carollo, Jiannis K. Pachos. 2005-08-04. Geometric phases and criticality in spin chain systems. https://doi.org/10.1103/physrevlett.95.157203

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