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

Shi-Liang Zhu
Phys. Rev. Lett. 96, 077206 – Published 23 February 2006

Abstract

We show that the 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 the geometric phase is nonanalytical and its derivative with respect to the field strength diverges at the critical magnetic field. Furthermore, the universality in the critical properties of the geometric phase in a family of models is verified. In addition, since the quantum phase transition occurs at a level crossing or avoided level crossing and these level structures can be captured by the Berry curvature, the established relation between the 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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  • Received 26 November 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.077206

©2006 American Physical Society

Authors & Affiliations

Shi-Liang Zhu

  • FOCUS Center and MCTP, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • School of Physics and Telecommunication Engineering, Laboratory of Photonic Information Technology, South China Normal University, Guangzhou, China

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Issue

Vol. 96, Iss. 7 — 24 February 2006

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