algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
quantum algorithms:
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The introduction of the parafermions 1 in the context of statistical models and conformal field theory [2] is perhaps one of the most significant conceptual advances in modern theoretical physics DGZ02
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We caution the reader that the level- Read-Rezayi wavefunction 10 is constructed from a conformal field theory (CFT) known as the parafermions of Zamolodchikov-Fateev 32 type which is closely related to the Chern-Simons theory, and which is a different object from the parafermions of the Fradkin-Kadanoff-Fendley type 46. To avoid confusion we emphasise at this point that within this paper, all mention of parafermions will refer to Fradkin-Kadanoff-Fendley type. CFRS00, p. 1
In fact the Zamolodchikov-Fateev parafermions represent a critical point at the transition into a phase described by Fradkin-Kadanoff-Fendley parafermions. CFRS00, p. 9
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Related to the fractional superstring.
Introducing parafermion 2d CFT:
Further discussion:
Eduardo Fradkin, Leo P. Kadanoff, Disorder variables and para-fermions in two-dimensional statistical mechanics, Nuclear Physics B 170 1 (1980) 1-15 doi:10.1016/0550-3213(80)90472-1
Paul Fendley, Free parafermions, J. Phys. A 47 (2014) 075001 arXiv:1310.6049, doi:10.1088/1751-8113/47/7/075001
Paul Fendley, Parafermionic edge zero modes in -invariant spin chains, J. Stat. Mech. (2012) P11020 doi:10.1088/1742-5468/2012/11/P11020
More general construction as coset-WZW models (2d current algebra CFT):
Doron Gepner, New conformal field theories associated with Lie algebras and their partition functions, Nuclear Physics B 290 (1987) 10-24 [doi:10.1016/0550-3213(87)90176-3]
Peter Bouwknegt, Bolin Han, Coupled free fermion conformal field theories [arXiv:2403.03471]
Relating parafermions to the affine su(2)-current algebra/WZW model (su(2)-anyons):
T. Jayaraman, Kumar S. Narain, M. H. Sarmadi, WZW and parafermion models on the torus, Nuclear Physics B 343 2 (1990) 418-449 doi:10.1016/0550-3213(90)90477-U
Daniel Cabra, Spinons and parafermions in fermion cosets, talk at International Seminar dedicated to the memory of D. V. Volkov, Kharkov (January 5-7, 1997) arXiv:hep-th/9704015
Daniel C. Cabra, Eduardo Fradkin, G. L. Rossini, F. A. Schaposnik, Section 4 of: Non-Abelian fractional quantum Hall states and chiral coset conformal field theories, International Journal of Modern Physics A 15 30 (2000) 4857-4870 doi:10.1142/S0217751X00002354, arXiv:cond-mat/9905192
On boundary conditions (BCFT/D-branes) for the gauged WZW model via parafermions:
See also:
As models for su(2)-anyon wavefunctions:
Nicholas Read, Edward Rezayi, Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level, Phys. Rev. B 59 (1999) 8084 doi:10.1103/PhysRevB.59.8084
David J. Clarke, Jason Alicea, Kirill Shtengel . Exotic non-Abelian anyons from conventional fractional quantum Hall states, Nature Communications 4 1348 (2013) doi: 10.1038/ncomms2340 (2013)
An integrable model for -parafermions:
Alexei M. Tsvelik, An integrable model with parafermion zero energy modes, Phys Rev. Lett. 113 066401 (2014) arXiv:1404.2840, doi:10.1103/PhysRevLett.113.066401
Alexei M. Tsvelik, parafermion zero modes without Fractional Quantum Hall effect arXiv:1407.4002
Daniel Borcherding, Non-Abelian quasi-particles in electronic systems, Hannover 2018 doi:10.15488/4280
Relation to topological phases of matter with topological order:
Jason Alicea, Paul Fendley, Topological phases with parafermions: theory and blueprints, Annual Review of Condensed Matter Physics 7 (2016) 119-139 doi:10.1146/annurev-conmatphys-031115-011336
Fernando Iemini, Christophe Mora, Leonardo Mazza, Topological phases of parafermions: a model with exactly-solvable ground states, Phys. Rev. Lett. 118 170402 (2017) arXiv;1611.00832, doi:10.1103/PhysRevLett.118.170402
On twisted parafermions:
Last revised on May 29, 2024 at 06:36:48. See the history of this page for a list of all contributions to it.