Abelian topological order on lattice enriched with electromagnetic background. (English) Zbl 1465.81079
The author introduces a construction of effective theories for a class of abelian topological orders on a 3D spacetime lattice with electromagnetic background. The author does this by gauging 1-form \(\mathbb{Z}\) symmetries, and in doing so, further insights are obtained, including the spin-c nature of the background field when the topological order is fermionic. This gauging of 1-form symmetries is similar to the Villain model.The Hall conductivity is also discussed. Some of the effective lattice theories can be mapped to microscopic Hamiltonians on a spatial lattice. The author also makes an explicit connection between the lattice construction and the doubled \(U(1)\) Chern-Simons path integral in the continuum. When the assumption of global symmetry is removed, the construction reduces to the Dijkgraaf-Witten model of associated abelian topological orders.
Reviewer: Eric Stachura (Marietta)
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 06B30 | Topological lattices |
| 81Q80 | Special quantum systems, such as solvable systems |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 81S40 | Path integrals in quantum mechanics |
| 82D25 | Statistical mechanics of crystals |
| 20H15 | Other geometric groups, including crystallographic groups |
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