Order Parameter for Symmetry-Protected Phases in One Dimension

Jutho Haegeman, David Pérez-García, Ignacio Cirac, and Norbert Schuch
Phys. Rev. Lett. 109, 050402 – Published 31 July 2012
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Abstract

We introduce an order parameter for symmetry-protected phases in one dimension which allows us to directly identify those phases. The order parameter consists of stringlike operators and swaps, but differs from conventional string order operators in that it only depends on the symmetry but not on the state. We verify our framework through numerical simulations for the SO(3) invariant spin-1 bilinear-biquadratic model which exhibits a dimerized and a Haldane phase, and find that the order parameter not only works very well for the dimerized and the Haldane phase, but it also returns a distinct signature for gapless phases. Finally, we discuss possible ways to measure the order parameter in experiments with cold atoms.

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  • Received 2 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.050402

© 2012 American Physical Society

Authors & Affiliations

Jutho Haegeman1, David Pérez-García2, Ignacio Cirac3, and Norbert Schuch4,5

  • 1Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
  • 2Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, E-28040 Madrid, Spain
  • 3Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany
  • 4Institut für Quanteninformation, RWTH Aachen, D-52056 Aachen, Germany
  • 5Institute for Quantum Information, California Institute of Technology, MC 305-16, Pasadena California 91125, USA

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Issue

Vol. 109, Iss. 5 — 3 August 2012

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