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Title: Symmetry Protected Topological Insulator of 3d bosons via Dyon Condensation: The 'Statistical Witten Effect'
Originating Office: IAS
Speaker: Fisher, M.P.A.
Issue Date: 14-Dec-2012
Event Date: 14-Dec-2012
Group/Series/Folder: Record Group 8.15 - Institute for Advanced Study
Series 3 - Audio-visual Materials
Location: 8.15:3 box 1.8
Notes: IAS Asia Pacific Workshop on Condensed Matter Physics. Talk no. 4
Title from title slide.
Host: Institute for Advanced Study.
Sponsor: The Collaborative Research Fund (CRF), The Research Grants Council (RGC).
Abstract: Electron topological insulators discovered theoretically by C. Kane are members of a broad class of 'symmetry protected topological' (SPT) phases of fermions and bosons which possess distinctive surface behavior protected by bulk symmetries. For 1d and 2d SPT's the surfaces are either gapless or symmetry broken, while in 3d, gapped symmetry-respecting surfaces with (intrinsic) 2d topological order are also possible. The electromagnetic response of (some) SPT's can provide an important characterization, as illustrated by the Witten effect in 3d electron topological insulators - an external magnetic monopole acquires a quantized half-odd integer polarization charge - as shown by Zhang et.al.. A classification of free fermions SPT's is possible, and a group cohomology classification has been proposed for bosonic SPT's by XG Wen et.al.. Moreover, 2d bosonic SPT's can be accessed dynamically using quantum Hall (K-matrix) technology, but 3d bosonic SPT's are less well understood. In an important advance, Vishwanath and Senthil (VS) obtained the 2d surface properties of some 3d bosonic SPT's using a 'dimensionality-bootstrap' approach, but the bulk 3d field theory is less clear (to me). Together with M. Metlitski and C. Kane, we have recently developed a new approach to access novel 3d boson phases. Within a U(1) parton-gauge-theory representation the bosonic partons and magnetic monopoles can be combined to form dyons, and a subsequent dyon condensation can lead to exotic new phases including some 3d bosonic SPT's. We thereby can obtain a 3d field theory for a bosonic SPT with both time-reveral and charge conservation symmetries, a theory which supports a gapped, symmetry-unbroken 2d surface with topological order - a toric code with charge one-half anyons - consistent with the VS bootstrap construction. The 3d electromagnetic response of this bosonic SPT phase is quite remarkable - an external magnetic monopole can remain charge neutral, but is statistically transmuted becoming a fermion - a 'statistical Witten effect' that characterizes the phase.
Duration: 43 min.
Appears in Series:8.15:3 - Audio-visual Materials
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