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We show that geometric phase of the ground state in the XY model obeysscaling behavior in the vicinity of a quantum phase transition. In particularwe find that geometric phase is non-analytical and its derivative with respectto the field strength diverges at the critical magnetic field. Furthermore,universality in the critical properties of the geometric phase in a family ofmodels is verified. In addition, since quantum phase transition occurs at alevel crossing or avoided level crossing and these level structures can becaptured by Berry curvature, the established relation between geometric phaseand quantum phase transitions is not a specific property of the XY model, but avery general result of many-body systems.Comment: 4 page

physical review letters

Scaling of Geometric Phases Close to the Quantum Phase Transition in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:math>Spin Chain

Scaling of Geometric Phases Close to the Quantum Phase Transition in theXYSpin Chain