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A holographic quantum Hall model at integer filling

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Abstract

We construct a holographic model of a system of strongly-coupled fermions in 2 + 1 dimensions based on a D8-brane probe in the background of D2-branes. The Minkowski embeddings of the D8-brane represent gapped quantum Hall states with filling fraction one. By computing the conductivity and phase structure, we find results qualitatively similar to the experimental observations and also to the recent D3-D7’ model.

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References

  1. S. Girvin, The Quantum Hall Effect: Novel Excitations and Broken Symmetries, Les Houches Lectures, Topological Aspects of Low Dimensional Systems, (1998) [cond-mat/9907002].

  2. V.J. Goldman and B. Su, Resonant Tunneling in Quantum Hall Effect: Measurement of Fractional Charge, Science 267 (1995) 1010.

    Article  ADS  Google Scholar 

  3. R. de Picciotto et al., Direct observation of a fractional charge, Nature 389 (1997) 162 [SPIRES].

    Article  ADS  Google Scholar 

  4. I. Neder, M. Heiblum, Y. Levinson, D. Mahalu and V. Umansky, Unexpected Behavior in a Two-Path Electron Interferometer, Phys. Rev. Lett. 96 (2006) 016804.

    Article  ADS  Google Scholar 

  5. E. Keski-Vakkuri and P. Kraus, Quantum Hall Effect in AdS/CFT, JHEP 09 (2008) 130 [ar**v:0805.4643] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [ar**v:0911.3586] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. K. Goldstein et al., Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [ar**v:1007.2490] [SPIRES].

    Article  ADS  Google Scholar 

  8. 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 [ar**v:1008.1917] [SPIRES].

    Article  ADS  Google Scholar 

  9. E. Gubankova et al., Holographic fermions in external magnetic fields, ar**v:1011.4051 [SPIRES].

  10. J.H. Brodie, L. Susskind and N. Toumbas, How Bob Laughlin tamed the giant graviton from Taub-NUT space, JHEP 02 (2001) 003 [hep-th/0010105] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. O. Bergman, Y. Okawa and J.H. Brodie, The stringy quantum Hall fluid, JHEP 11 (2001) 019 [hep-th/0107178] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  12. S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, hep-th/0107200 [SPIRES].

  13. S.-J. Rey, String theory on thin semiconductors: Holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [ar**v:0911.5295] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  14. J.L. Davis, P. Kraus and A. Shah, Gravity Dual of a Quantum Hall Plateau Transition, JHEP 11 (2008) 020 [ar**v:0809.1876] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. R.C. Myers and M.C. Wapler, Transport Properties of Holographic Defects, JHEP 12 (2008) 115 [ar**v:0811.0480] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. M. Fujita, W. Li, S. Ryu and T. Takayanagi, Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States and Hierarchy, JHEP 06 (2009) 066 [ar**v:0901.0924] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. Y. Hikida, W. Li and T. Takayanagi, ABJM with Flavors and FQHE, JHEP 07 (2009) 065 [ar**v:0903.2194] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. J. Alanen, E. Keski-Vakkuri, P. Kraus and V. Suur-Uski, AC Transport at Holographic Quantum Hall Transitions, JHEP 11 (2009) 014 [ar**v:0905.4538] [SPIRES].

    Article  ADS  Google Scholar 

  19. D.K. Hong and H.-U. Yee, Holographic aspects of three dimensional QCD from string theory, JHEP 05 (2010) 036 [ar**v:1003.1306] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall Effect in a Holographic Model, JHEP 10 (2010) 063 [ar**v:1003.4965] [SPIRES].

    Article  ADS  Google Scholar 

  21. A. Belhaj, N.-E. Fahssi, E.H. Saidi and A. Segui, Embedding Fractional Quantum Hall Solitons in M-theory Compactifications, ar**v:1007.4485 [SPIRES].

  22. M. Fujita, M5-brane Defect and QHE in AdS 4 × N (1, 1)/N = 3 SCFT, ar**v:1011.0154 [SPIRES].

  23. T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  24. T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  25. A.M. Dykhne and I.M. Ruzin, Theory of the fractional quantum Hall effect: The two-phase model, Phys. Rev. B 50 (1994) 2369.

    ADS  Google Scholar 

  26. M. Hilke, D. Shahar, S.H. Song, D.C. Tsui, Y.H. **e and D. Monroe, Quantized Hall Insulator: A New insulator in Two-Dimensions, Nature 395 (1998) 675 [cond-mat/9810172].

    Article  ADS  Google Scholar 

  27. M. Hilke, D. Shahar, S. H. Song, D. C. Tsui, Y. H. **e and M. Shayegan, Semicircle: An exact relation in the integer and fractional quantum Hall effect, Europhys. Lett. 46 (1999) 775 [cond-mat/9810217].

    Article  ADS  Google Scholar 

  28. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  29. D. Marolf and S.F. Ross, Boundary conditions and new dualities: Vector fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. O. Domenech, M. Montull, A. Pomarol, A. Salvio and P.J. Silva, Emergent Gauge Fields in Holographic Superconductors, JHEP 08 (2010) 033 [ar**v:1005.1776] [SPIRES].

    Article  ADS  Google Scholar 

  31. K. Maeda, M. Natsuume and T. Okamura, On two pieces of folklore in the AdS/CFT duality, Phys. Rev. D 82 (2010) 046002 [ar**v:1005.2431] [SPIRES].

    ADS  Google Scholar 

  32. O. Bergman, G. Lifschytz and M. Lippert, Magnetic properties of dense holographic QCD, Phys. Rev. D 79 (2009) 105024 [ar**v:0806.0366] [SPIRES].

    ADS  Google Scholar 

  33. N. Jokela, G. Lifschytz and M. Lippert, Magneto-roton excitation in a holographic quantum Hall fluid, JHEP 02 (2011) 104 [ar**v:1012.1230] [SPIRES].

    Article  ADS  Google Scholar 

  34. K. Ghoroku, M. Ishihara and A. Nakamura, D3/D7 holographic Gauge theory and Chemical potential, Phys. Rev. D 76 (2007) 124006 [ar**v:0708.3706] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  35. D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [ar**v:0709.1225] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [ar**v:0705.3870] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [ar**v:0708.1994] [SPIRES].

    ADS  Google Scholar 

  38. G. Lifschytz and M. Lippert, Anomalous conductivity in holographic QCD, Phys. Rev. D 80 (2009) 066005 [ar**v:0904.4772] [SPIRES].

    ADS  Google Scholar 

  39. B. Tausendfreund and K. von Klitzing, Analysis of quantized Hall resistance at finite temperatures, Suf. Sci. 142 (1983) 220.

    Article  Google Scholar 

  40. W. Pan et al., Exact Quantization of Even-Denominator Fractional Quantum Hall State at ν = 5/2 Landau Level Filling Factor, Phys. Rev. Lett. 83 (1999) 3530 [cond-mat/9810172].

    Article  ADS  Google Scholar 

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Correspondence to Matthew Lippert.

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Ar**v ePrint: 1101.3329

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Jokela, N., Järvinen, M. & Lippert, M. A holographic quantum Hall model at integer filling. J. High Energ. Phys. 2011, 101 (2011). https://doi.org/10.1007/JHEP05(2011)101

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