Wave functions of bosonic symmetry protected topological phases
Author(s)Xu, Cenke; Todadri, Senthil
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We study the structure of the ground-state wave functions of bosonic symmetry protected topological (SPT) insulators in three space dimensions. We demonstrate that the differences with conventional insulators are captured simply in a dual vortex description. As an example, we show that a previously studied bosonic topological insulator with both global U(1) and time-reversal symmetry can be described by a rather simple wave function written in terms of dual “vortex ribbons.” The wave function is a superposition of all the vortex-ribbon configurations of the boson, and a factor (−1) is associated with each self-linking of the vortex ribbons. This wave function can be conveniently derived using an effective field theory of the SPT phase in the strong-coupling limit, and it naturally explains all the phenomena of this SPT phase discussed previously. The ground-state structure for other three-dimensional (3D) bosonic SPT phases are also discussed similarly in terms of vortex loop gas wave functions. We show that our methods reproduce known results on the ground-state structure of some 2D SPT phases.
DepartmentMassachusetts Institute of Technology. Department of Physics
Physical Review B
American Physical Society
Xu, Cenke, and Senthil Todadri. “Wave Functions of Bosonic Symmetry Protected Topological Phases.” Phys. Rev. B 87, no. 17 (May 2013). ©2013 American Physical Society.
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