Journal
PHYSICAL REVIEW B
Volume 87, Issue 17, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.87.174412
Keywords
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Funding
- Alfred P. Sloan Foundation
- David and Lucile Packard Foundation
- Hellman Family Foundation
- NSF [DMR-1151208, DMR-1005434]
- Simons Foundation [229736]
- Direct For Mathematical & Physical Scien [1151208] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1005434] Funding Source: National Science Foundation
- Division Of Materials Research [1151208] Funding Source: National Science Foundation
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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.
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