Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
By Ashvin Vishwanath, T. Senthil. 2012
302 citations recorded by the source corpus.
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order and are bosonic analogs of free fermion topological insulators and superconductors. While a formal cohomology based classification of such states was recently discovered, their physical properties remain mysterious. Here we develop a field theoretic description of several of these states and show that they possess unusual surface states, which if gapped, must either break the underlying symmetry, or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two dimensional theory. While this is the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by quantized magnetoelectric response \theta, which, somewhat surprisingly, is an odd multiple of 2\pi. Two different surface theories are shown to capture these phenomena - the first is a nonlinear sigma model with a topological term. The second invokes vortices on the surface that transform under a projective representation of the symmetry group. A bulk field theory consistent with these properties is identified, which is a multicomponent `BF' theory supplemented, crucially, with a topological term. A possible topological phase characterized by the thermal analog of the magnetoelectric effect is also discussed.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/35b25ccde65d0d91b45fa4752d339649125684b6
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Generalized Symmetries in Condensed Matter (2022, unknown): “cannot be trivial, since it has to cancel the variation of the bulk under the symmetry transformation: it has to be either (52)”
- Topological Phases Protected by Point Group Symmetry (2016, background): “For bosonic systems with Z2 only or Z T 2 only, the classification of SPT phases is Z2 in d 1⁄4 1 [6,7,10,11] and Z2 × Z2 in d 1⁄4 3 [42,52,53,73].”
- Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “Those SPT states are referred to as beyondgroup-cohomology SPT states [30].”
- Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface (2015, background): “When [O] is a nontrivial, the symmetry fractionalization class is anomalous and it can only appear as the surface termination of a 3D SPT phase [8, 18].”
- Gapped boundary phases of topological insulators via weak coupling (2016, background): “4) by 2 (or by any even integer), we get a T-invariant theory that no longer needs a spin structure and might be a boundary state for the bosonic topological insulators of [32].”
- Deconfined quantum critical points: symmetries and dualities (2017, background): “Finally, deconfined critical field theories also arise in the context of phase transitions between trivial and SPT phases [46,47,58].”
- On 2-group global symmetries and their anomalies (2018, background): “The background-coupled theory with such anyons is also called the eTmT state [61].”