Relationship between the Parameters of the Second Virial Coefficient of Non-Abelian Anyons and the Two-Parametric Fractional Statistics
DOI:
https://doi.org/10.15407/ujpe66.7.595Keywords:
virial coefficient, non-Abelian anyons, non-additive/incomplete two-parametric statistics, Haldane–Wu fractional statistics, Polychronakos fractional statisticsAbstract
A relationship between the parameters of the second virial coefficient for the system of non- Abelian anyons and two-parametric modifications of the Haldane–Wu and Polychronakos fractional statistics has been demonstrated. Parameters that can approximately describe non-Abelian anyons using the indicated statistics types are calculated. The limit at which the non-additivity/incompleteness parameter q tends to unity is considered.
References
J.M. Leinaas, J. Myrheim. On the theory of identical particles. Nuovo Cimento 37B, 1 (1977).
https://doi.org/10.1007/BF02727953
F. Wilczek. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957 (1982).
https://doi.org/10.1103/PhysRevLett.49.957
B.I. Halperin. Statistics of quasiparticles and the hierarchy of fractional quantized Hall states. Phys. Rev. Lett. 52, 1583 (1984).
https://doi.org/10.1103/PhysRevLett.52.1583
D. Arovas, J.R. Schrieff er, F. Wilczek. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722 (1984).
https://doi.org/10.1103/PhysRevLett.53.722
A.E.B. Nielsen. Anyon braiding in semianalytical fractional quantum Hall lattice models. Phys. Rev. B 91, 041106 (2015).
https://doi.org/10.1103/PhysRevB.91.041106
E. Shech. Two approaches to fractional statistics in the quantum Hall effect: Idealizations and the curious case of the anyon. Found. Phys. 45, 1063 (2015).
https://doi.org/10.1007/s10701-015-9899-0
A.Yu. Kitaev. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003).
https://doi.org/10.1016/S0003-4916(02)00018-0
V. Lahtinen, J.K. Pachos. A short introduction to topological quantum computation. SciPost Phys. 3, 021 (2017).
https://doi.org/10.21468/SciPostPhys.3.3.021
F.E. Camino, W. Zhou, V.J. Goldman. Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics. Phys. Rev. B 72, 075342 (2005).
https://doi.org/10.1103/PhysRevB.72.075342
C. Weeks, G. Rosenberg, B. Seradjeh, M. Franz. Anyons in a weakly interacting system. Nature Phys. 3, 797 (2007).
https://doi.org/10.1038/nphys730
T. Keilmann, S. Lanzmich, I. McCulloch, M. Roncaglia. Statistically induced phase transitions and anyons in 1D optical lattices. Nature Commun. 2, 361 (2011).
https://doi.org/10.1038/ncomms1353
G. Moore, N. Read. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360 362 (1991).
https://doi.org/10.1016/0550-3213(91)90407-O
L. Jacak, P. Sitko, K. Wieczorek, A. W'ojs. Quantum Hall Systems: Braid Groups, Composite Fermions, and Fractional Charge (Oxford Univ Press, 2003).
https://doi.org/10.1093/acprof:oso/9780198528708.001.0001
M. Dolev, M. Heiblum, V. Umansky, A. Stern, D. Mahalu. Observation of a quarter of an electron charge at the v = 5/2 quantum Hall state. Nature 452, 829 (2008).
https://doi.org/10.1038/nature06855
R.L. Willett, L.N. Pfeiffer, K.W. West. Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations. Proc. Natl. Acad. Sci. 106, 8853 (2009).
https://doi.org/10.1073/pnas.0812599106
W. Bishara, P. Bonderson, C. Nayak, K. Shtengel, J.K. Slingerland. Interferometric signature of non-Abelian anyons. Phys. Rev. B 80, 155303 (2009).
https://doi.org/10.1103/PhysRevB.80.155303
F. Mancarella, A. Trombettoni, G. Mussardo. Statistical mechanics of an ideal gas of non-Abelian anyons. Nucl. Phys. B 867, 950 (2013).
https://doi.org/10.1016/j.nuclphysb.2012.10.020
A.P. Polychronakos. Virial coefficients of non-Abelian anyons. Phys. Rev. Lett. 84, 1268 (2000).
https://doi.org/10.1103/PhysRevLett.84.1268
T. Lee. On statistical mechanics of non-Abelian Chern-Simons particles, preprint arXiv: hep-th/9601018 (1996).
A. Rovenchak. Two-parametric fractional statistics models for anyons. Eur. Phys. J. B 87, 175 (2014).
https://doi.org/10.1140/epjb/e2014-50171-8
C. Tsallis. What are the numbers that experiments provide? Qu'ımica Nova 17, 468 (1994).
J. Naudts. The q-exponential family in statistical physics. J. Phys.: Conf. Ser. 201, 012003 (2010). https://doi.org/10.1088/1742-6596/201/1/012003
S. Umarov, C. Tsallis, S. Steinberg. On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan J. Math. 76, 307 (2008). https://doi.org/10.1007/s00032-008-0087-y
B. Rosenow, I.P. Levkivskyi, B.I. Halperin. Current correlations from a mesoscopic anyon collider Phys. Rev. Lett. 116, 15 (2016). https://doi.org/10.1103/PhysRevLett.116.156802
H. Bartolomei et al. Fractional statistics in anyon collisions. Science 368, 6487 (2020). https://doi.org/10.1126/science.aaz5601
A. Khare. Fractional Statistics and Quantum Theory (World Scientifi c, 2005). https://doi.org/10.1142/5752
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
