Gapped boundary phases of topological insulators via weak coupling

By N. Seiberg, E. Witten. 2016

230 citations recorded by the source corpus.

The standard boundary state of a topological insulator in 3 + 1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological order. Our models are weakly coupled and all the dynamics is explicit. We rederive some known boundary states of topological insulators and construct new ones. Consistency with the standard spin/charge relation of condensed matter physics places a nontrivial constraint on models.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f886a38f00c954ed9fc26ae9662a8bfa9607540c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Clay Córdova
2. Po-Shen Hsin
3. F. Benini
4. N. Seiberg
5. D. Gaiotto
6. Juven C. Wang
7. E. Witten
8. Ho Tat Lam

In Condensed Matter Physics

1. F. Benini
2. Clay Córdova
3. Po-Shen Hsin
4. N. Seiberg
5. E. Witten
6. D. Gaiotto
7. Pavel Putrov
8. Juven C. Wang

Citations in the corpus

• The "parity" anomaly on an unorientable manifold (2016, methodology): “41) in [22], where X was assumed to be orientable and a coupling to electromagnetism was incorporated.”
• Particle-vortex duality in topological insulators and superconductors (2016, background): “3 of [23] that the coupling of ψ to 2aμ is not correct, since issues of Dirac quantization mean that it doesn’t give the right anomaly.”
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, methodology): “We use the description of the Ising TQFT in terms of Chern-Simons theory (CS) U(2)2,−4 ∼= (SU(2)2 × U(1)−4)/Z2 from [87].”
• On 2-group global symmetries and their anomalies (2018, methodology): “From the spins (35)This uses the following property: a duality between two non-spin 3d TQFTs each tensored with the invertible spin-TQFT {1, ψ} [57] implies that the non-spin TQFTs themselves are dual, if and only if their framing anomalies differ by a multiple of 8 [58].”
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, unknown): “[41] in examples.”
• Symmetries and strings of adjoint QCD2 (2020, unknown): “a fermionic SPT phases) [93–96].”
• Theta, time reversal and temperature (2017, background): “For more sophisticated examples see, for example, [5,6] and references therein.”
• Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, background): “where a, ã are dynamical U(1) gauge fields (more precisely they are spinc connections [49]) while Ψ1,2, χ1,2 are complex fermions.”
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics (2016, unknown): “An elegant although formal way to capture these relations is to introduce a spinc connection 6 A that couples to the conserved charge carried by the fermions [41,51].”
• Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “Appendix C of [33], Appendix B of [34], and also [6].”
• Chern-Simons-matter dualities with SO and USp gauge groups (2016, methodology): “The special case U(1)2 is known as the “fermion/semion theory” [57] and was discussed recently in [35,28].”