nLab Kramers-Wannier duality

Idea

Kramers-Wannier duality is a duality in physics of the Ising model 2d CFT.

Related concepts

• Euclidean field theory

References

Named after:

• Hendrik A. Kramers, Gregory H. Wannier: Statistics of the Two-Dimensional Ferromagnet. Part I, Phys. Rev. 60 (1941) 252 [doi:10.1103/PhysRev.60.252]

See also:

• Wikipedia: Kramers-Wannier duality

Discussion by defect QFT in the context of the FRS-formalism with defects:

• Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel, Christoph Schweigert, Kramers-Wannier duality from conformal defects, Phys.Rev.Lett. 93 (2004) 070601 (arXiv:cond-mat/0404051)

Here in FRS-formalism a 2d CFT is formalized as a boundary field theory to a 3d TQFT based on the Turaev-Viro model, similar to the CS-WZW correspondence.

Another discussion involving these keywords:

• Daniel Freed, Constantin Teleman, Topological dualities in the Ising model (arXiv:1806.00008)

Realization in lattice field theory:

• David Aasen, Roger S. K. Mong, Paul Fendley, Topological Defects on the Lattice I: The Ising model, J. Phys. A: Math. Theor. 49 (2016) 354001 [arXiv:1601.07185, doi:10.1088/1751-8113/49/35/354001]

• David Aasen, Paul Fendley, Roger S. K. Mong, Topological Defects on the Lattice: Dualities and Degeneracies [arXiv:2008.08598, inspire:1812559]

• Mao Tian Tan, Yifan Wang, Aditi Mitra, Topological Defects in Floquet Circuits [arXiv:2206.06272]

and simulation on a quantum computer:

• Sutapa Samanta, Derek S. Wang, Armin Rahmani, Aditi Mitra, Isolated Majorana mode in a quantum computer from a duality twist [arXiv:2308.02387]

See also:

• Akash Sinha, Pramod Padmanabhan, Vladimir Korepin: When Is Kramers-Wannier Duality Invertible? [arXiv:2609.20090]