Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry

Peng Ye University of Illinois at Urbana-Champaign Taylor L. Hughes University of Illinois at Urbana-Champaign Joseph Maciejko University of Alberta, Canadian Institute for Advanced Research Eduardo Fradkin University of Illinois at Urbana-Champaign

Publications of CMSA of Harvard mathscidoc:1702.38070

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e. the deconfined phase of ℤ2 gauge theory) is a U(1)×U(1) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a new route to constructing exotic 3D gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1)×U(1) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1)×U(1) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-H\"uckel-like screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ≠π, the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (𝖢𝗁𝖺𝗋𝗅𝖾𝗌) of 3D Abelian topological phases. We show that line twist defects, which realize 𝖢𝗁𝖺𝗋𝗅𝖾𝗌 transformations, exhibit non-Abelian fusion properties.
No keywords uploaded!
[ Download ] [ 2017-02-08 00:39:42 uploaded by dmuoio ] [ 402 downloads ] [ 0 comments ]
@inproceedings{pengcomposite,
  title={Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry},
  author={Peng Ye, Taylor L. Hughes, Joseph Maciejko, and Eduardo Fradkin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208003942097791297},
}
Peng Ye, Taylor L. Hughes, Joseph Maciejko, and Eduardo Fradkin. Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208003942097791297.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved