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Hidden order and flux attachment in symmetry-protected topological phases: A Laughlin-like approach

Zohar Ringel and Steven H. Simon
Phys. Rev. B 91, 195117 – Published 12 May 2015

Abstract

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here, we introduce a new approach for generating SPT ground states, based on a generalization of the Laughlin wave function. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wave functions obtained in this manner and group cohomology wave functions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wave function obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.

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  • Received 21 January 2015
  • Revised 22 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.195117

©2015 American Physical Society

Authors & Affiliations

Zohar Ringel and Steven H. Simon

  • Theoretical Physics, Oxford University, 1, Keble Road, Oxford OX1 3NP, United Kingdom

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Issue

Vol. 91, Iss. 19 — 15 May 2015

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