nLab defect anyons -- references

Defect anyons

Often the concept of anyons is introduced as if a generalization of perturbative quanta like fundamental bosons and fermions. But many (concepts of) types of anyons are really solitonic$\;$defects such as vortices.

The general concept of braiding of defects in solid state physics:

• N. David Mermin, The topological theory of defects in ordered media, Rev. Mod. Phys. 51 (1979) 591 $[$doi:10.1103/RevModPhys.51.591$]$

  (including a review of basic homotopy theory)

and more specifically for vortices:

• Hoi-Kwong Lo, John Preskill, Non-Abelian vortices and non-Abelian statistics, Phys. Rev. D 48 (1993) 4821 $[$doi:10.1103/PhysRevD.48.4821$]$

Explicit discussion in terms of anyons:

• Alexei Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321 1 (2006) 2-111 $[$doi:10.1016/j.aop.2005.10.005$]$

  Anyonic particles are best viewed as a kind of topological defects that reveal nontrivial properties of the ground state. $[$p. 4$]$

Concrete vortex$\;$anyons in Bose-Einstein condensates:

• B. Paredes, P. Fedichev, J. Ignacio Cirac, Peter Zoller: 1/2-Anyons in small atomic Bose-Einstein condensates, Phys. Rev. Lett. 87 (2001) 010402 [doi:10.1103/PhysRevLett.87.010402, arXiv:cond-mat/0103251]

• Julien Garaud, Jin Dai, Antti J. Niemi, Vortex precession and exchange in a Bose-Einstein condensate, J. High Energ. Phys. 2021 157 (2021) $[$arXiv:2010.04549$]$

• Thomas Mawson, Timothy Petersen, Joost Slingerland, Tapio Simula, Braiding and fusion of non-Abelian vortex anyons, Phys. Rev. Lett. 123 (2019) 140404 $[$doi:10.1103/PhysRevLett.123.140404$]$

and in (other) superfluids:

• Yusuke Masaki, Takeshi Mizushima, Muneto Nitta, Non-Abelian Half-Quantum Vortices in 3P2 Topological Superfluids $[$arXiv:2107.02448$]$

and in condensates of non-defect anyons:

• Michele Correggi, Romain Duboscq, Douglas Lundholm, Nicolas Rougerie, Vortex patterns in the almost-bosonic anyon gas, Europhys. Lett. 126 (2019), 20005 $[$arXiv:1901.10739, doi:10.1209/0295-5075/126/20005$]$

See also Ahn, Park & Yang 19 who refer to the band nodes in the Brillouin torus of a semi-metal as “vortices in momentum space”.

And see at defect brane.