Holographic anyonization: a systematic approach

  • Matthias Ihl
  • Niko Jokela
  • Tobias Zingg
Open Access
Regular Article - Theoretical Physics


Anyons have garnered substantial interest theoretically as well as experimentally. Due to the intricate nature of their interactions, however, even basic notions such as the equation of state for any kind of anyon gas have eluded a profound understanding so far. Using holography as a guiding principle, we propose a general method for an alternative quantization of electromagnetic degrees of freedom in the gravitational dual to obtain an effective physical description of strongly correlated anyonic systems. We then demonstrate the application of this prescription in a toy model of an anyonic fluid at finite charge density and magnetic field, dual to a dyonic black brane in AdS 4, and compute the equation of state and various transport coefficients explicitly.


Holography and condensed matter physics (AdS/CMT) Anyons Gaugegravity correspondence 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    J.M. Leinaas and J. Myrheim, On the theory of identical particles, Nuovo Cim. B 37 (1977) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Rao, An anyon primer, hep-th/9209066 [INSPIRE].
  3. [3]
    A. Stern, Anyons and the quantum Hall effect: a pedagogical review, Ann. Phys. 323 (2008) 1.ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Y.-H. Chen, F. Wilczek, E. Witten and B.I. Halperin, On anyon superconductivity, Int. J. Mod. Phys. B 3 (1989) 1001 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    G.W. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360 (1991) 362 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    A. Yu. Kitaev, Fault tolerant quantum computation by anyons, Annals Phys. 303 (2003) 2 [quant-ph/9707021] [INSPIRE].
  7. [7]
    Y. Hosotani, Neutral and charged anyon fluids, Int. J. Mod. Phys. B 7 (1993) 2219 [cond-mat/9302002] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Yi and G.S. Canright, Spontaneous magnetization of anyons with long-range repulsion, Phys. Rev. B 47 (1993) 273.ADSCrossRefGoogle Scholar
  9. [9]
    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].
  10. [10]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].CrossRefMATHGoogle Scholar
  11. [11]
    A.V. Ramallo, Introduction to the AdS/CFT correspondence, Springer Proc. Phys. 161 (2015) 411 [arXiv:1310.4319] [INSPIRE].CrossRefMATHGoogle Scholar
  12. [12]
    E. Witten, SL(2, ℤ) action on three-dimensional conformal field theories with Abelian symmetry, in From fields to strings, volume 2, M. Shifman et al., World Scientific, Singapore (2005), hep-th/0307041 [INSPIRE].
  13. [13]
    H.-U. Yee, A note on AdS/CFT dual of SL(2, ℤ) action on 3 − D conformal field theories with U(1) symmetry, Phys. Lett. B 598 (2004) 139 [hep-th/0402115] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    N. Jokela, G. Lifschytz and M. Lippert, Holographic anyonic superfluidity, JHEP 10 (2013) 014 [arXiv:1307.6336] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Bayntun, C.P. Burgess, B.P. Dolan and S.-S. Lee, AdS/QHE: towards a holographic description of quantum Hall experiments, New J. Phys. 13 (2011) 035012 [arXiv:1008.1917] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  17. [17]
    M. Fujita, M. Kaminski and A. Karch, SL(2, ℤ) action on AdS/BCFT and Hall conductivities, JHEP 07 (2012) 150 [arXiv:1204.0012] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    M. Lippert, R. Meyer and A. Taliotis, A holographic model for the fractional quantum Hall effect, JHEP 01 (2015) 023 [arXiv:1409.1369] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall Effect in a Holographic Model, JHEP 10 (2010) 063 [arXiv:1003.4965] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    N. Jokela, G. Lifschytz and M. Lippert, Flowing holographic anyonic superfluid, JHEP 10 (2014) 21 [arXiv:1407.3794] [INSPIRE].ADSGoogle Scholar
  21. [21]
    D.K. Brattan and G. Lifschytz, Holographic plasma and anyonic fluids, JHEP 02 (2014) 090 [arXiv:1310.2610] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    D.K. Brattan, A strongly coupled anyon material, JHEP 11 (2015) 214 [arXiv:1412.1489] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    G. Itsios, N. Jokela and A.V. Ramallo, Cold holographic matter in the Higgs branch, Phys. Lett. B 747 (2015) 229 [arXiv:1505.02629] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    N. Jokela and A.V. Ramallo, Universal properties of cold holographic matter, Phys. Rev. D 92 (2015) 026004 [arXiv:1503.04327] [INSPIRE].ADSMathSciNetGoogle Scholar
  25. [25]
    G. Itsios, N. Jokela and A.V. Ramallo, Collective excitations of massive flavor branes, arXiv:1602.06106 [INSPIRE].
  26. [26]
    D. Bak and S.-J. Rey, Composite fermion metals from dyon black holes and S-duality, JHEP 09 (2010) 032 [arXiv:0912.0939] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].ADSGoogle Scholar
  28. [28]
    T. Zingg, Thermodynamics of dyonic lifshitz black holes, JHEP 09 (2011) 067 [arXiv:1107.3117] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    S.A. Hartnoll and P. Petrov, Electron star birth: a continuous phase transition at nonzero density, Phys. Rev. Lett. 106 (2011) 121601 [arXiv:1011.6469] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].ADSGoogle Scholar
  32. [32]
    T. Albash, C.V. Johnson and S. MacDonald, Holography, fractionalization and magnetic fields, Lect. Notes Phys. 871 (2013) 537 [arXiv:1207.1677] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    M. Blake, S. Bolognesi, D. Tong and K. Wong, Holographic dual of the lowest landau level, JHEP 12 (2012) 039 [arXiv:1208.5771] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    E. Gubankova, J. Brill, M. Cubrovic, K. Schalm, P. Schijven and J. Zaanen, Holographic description of strongly correlated electrons in external magnetic fields, Lect. Notes Phys. 871 (2013) 555 [arXiv:1304.3835] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    V. Giangreco M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Magnetic oscillations in a holographic liquid, Phys. Rev. D 91 (2015) 086008 [arXiv:1501.06459] [INSPIRE].ADSGoogle Scholar
  36. [36]
    C. Sträter, S.C.L. Srivastava and A. Eckardt, Floquet realization and signatures of one-dimensional anyons in an optical lattice, arXiv:1602.08384. .

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Centro de Física do Porto e Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do PortoPortoPortugal
  2. 2.Department of PhysicsUniversity of HelsinkiFinland
  3. 3.Helsinki Institute of PhysicsUniversity of HelsinkiFinland

Personalised recommendations