Scaling of geometric phases close to quantum phase transition in the XY chain

Details Scaling of geometric phases close to quantum phase transition in the XY chain Scaling of geometric phases close to quantum phase transition in the XY chain

2005-11-23

arxiv.org/abs/cond-mat/0511565v1

Phys. Rev. Lett. 96, 077206 (2006) (a slightly different version)

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1103/PhysRevLett.96.077206

We show that geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that geometric phase is non-analytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, universality in the critical properties of the geometric phase in a family of models is verified. In addition, since quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by Berry curvature, the established relation between geometric phase and quantum phase transitions is not a specific property of the XY model, but a very general result of many-body systems.

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