String Order and Symmetries in Quantum Spin Lattices

D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, and J. I. Cirac
Phys. Rev. Lett. 100, 167202 – Published 22 April 2008

Abstract

We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this connection is established, we provide a complete characterization of local symmetries in these states. The results allow us to understand in a straightforward way many of the properties of string order parameters, like their robustness or fragility under perturbations and their typical disappearance beyond strictly one-dimensional lattices. We propose and discuss an alternative definition, ideally suited for detecting phase transitions, and generalizations to two and more spatial dimensions.

  • Figure
  • Received 5 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.167202

©2008 American Physical Society

Authors & Affiliations

D. Pérez-García1, M. M. Wolf2, M. Sanz2, F. Verstraete3, and J. I. Cirac2

  • 1Departamento de Analisis Matematico, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 2Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, D-85748, Germany
  • 3Fakultät für Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

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Issue

Vol. 100, Iss. 16 — 25 April 2008

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