Skip to main content
SpringerLink
Log in

Quantum corrected phase diagram of holographic fermions

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study the phases of strongly correlated electron systems in two spatial dimensions in the framework of AdS4/CFT3 correspondence. The AdS (gravity) model consists of a Dirac fermion coupled to electromagnetic field and gravity. To classify the ground states of strongly correlated electrons on the CFT side and to construct the full phase diagram of the system, we construct a quantum many-body model of bulk fermion dynamics, based on the WKB approximation to the Dirac equation. At low temperatures, we find a quantum corrected approximation to the electron star where the edge is resolved in terms of wave functions extended fully through AdS. At high temperatures, the system exhibits a first order thermal phase transition to a charged AdS-RN black hole in the bulk and the emergence of local quantum criticality on the CFT side. This change from the third order transition experienced by the semi-classical electron star restores the intuition that the transition between the critical AdS-RN liquid and the finite density Fermi system is of van der Waals liquid–gas type.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].

    Article  MATH  Google Scholar 

  3. H.V. Löhneysen, A. Rosch, M. Vojta and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79 (2007) 1015 [cond-mat/0606317].

    Article  ADS  Google Scholar 

  4. M. Gurvitch and A.T. Fiory, Resistivity of La1.825 Sr0.175 CuO4 and Y Ba2 Cu3 O7 to 1100 K: Absence of saturation and its implications, Phys. Rev. Lett. 59 (1987) 1337.

    Article  ADS  Google Scholar 

  5. A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. O. DeWolfe, S.S. Gubser and C. Rosen, Fermi surfaces in maximal gauged supergravity, Phys. Rev. Lett. 108 (2012) 251601 [arXiv:1112.3036] [INSPIRE].

    Article  ADS  Google Scholar 

  7. A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and electric AdS solutions in string-and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].

    ADS  Google Scholar 

  9. M. Čubrović, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].

    ADS  Google Scholar 

  11. J.P. Gauntlett, J. Sonner and D. Waldram, Universal fermionic spectral functions from string theory, Phys. Rev. Lett. 107 (2011) 241601 [arXiv:1106.4694] [INSPIRE].

    Article  ADS  Google Scholar 

  12. 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].

    Article  ADS  Google Scholar 

  13. M. Čubrović, J. Zaanen and K. Schalm, Constructing the AdS Dual of a Fermi Liquid: AdS Black Holes with Dirac Hair, JHEP 10 (2011) 017 [arXiv:1012.5681] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  14. S. Sachdev, A model of a Fermi liquid using gauge-gravity duality, Phys. Rev. D 84 (2011) 066009 [arXiv:1107.5321] [INSPIRE].

    ADS  Google Scholar 

  15. R.C. Tolman, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev. D 55 (1939) 364.

    Article  ADS  MATH  Google Scholar 

  16. A. Allais, J. McGreevy and S.J. Suh, A quantum electron star, Phys. Rev. Lett. 108 (2012) 231602 [arXiv:1202.5308] [INSPIRE].

    Article  ADS  Google Scholar 

  17. S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: Fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  18. M. Cubrovic, Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair, Phys. Rev. D 84 (2011) 086002 [arXiv:1106.1798] [INSPIRE].

    ADS  Google Scholar 

  19. N. Iqbal, H. Liu and M. Mezei, Semi-local quantum liquids, JHEP 04 (2012) 086 [arXiv:1105.4621] [INSPIRE].

    Article  ADS  Google Scholar 

  20. S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  21. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].

    ADS  Google Scholar 

  22. E. Gubankova et al., Holographic fermions in external magnetic fields, Phys. Rev. D 84 (2011) 106003 [arXiv:1011.4051] [INSPIRE].

    ADS  Google Scholar 

  23. D.F. Mross, J. McGreevy, H. Liu and T. Senthil, A controlled expansion for certain non-Fermi liquid metals, Phys. Rev. B 82 (2010) 045121 [arXiv:1003.0894] [INSPIRE].

    Article  ADS  Google Scholar 

  24. G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. L.D. Landau and E.M. Lifshitz, Quantum Mechanics. Nonrelativistic theory, Nauka, Moskva Russia (1989).

  26. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Strange metal transport realized by gauge/gravity duality, Science 329 (2010) 1043 [INSPIRE].

    Article  ADS  Google Scholar 

  27. T. Hartman and S.A. Hartnoll, Cooper pairing near charged black holes, JHEP 06 (2010) 005 [arXiv:1003.1918] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. N. Iqbal and H. Liu, Real-time response in AdS/CFT with application to spinors, Fortsch. Phys. 57 (2009) 367 [arXiv:0903.2596] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. L.D. Landau and E.M. Lifshitz, Statistical Physics 2, Nauka, Moskva Russia (1978).

  30. N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [INSPIRE].

    ADS  Google Scholar 

  31. D. Voskresensky and A. Senatorov, Rearrangement of the vacuum in strong electric and gravitational fields, Sov. J. Nucl. Phys. 36 (1982) 208 [INSPIRE].

    Google Scholar 

  32. J.H. She and J. Zaanen, BCS Superconductivity in Quantum Critical Metals, Phys. Rev. B 80 (2009) 184518.

    Article  ADS  Google Scholar 

  33. V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  34. T. Faulkner and J. Polchinski, Semi-holographic Fermi liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  35. L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].

    ADS  Google Scholar 

  36. N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, arXiv:1110.3814 [INSPIRE].

  37. M. Čubrović, Holography, Fermi surfaces and criticality, Ph.D. Thesis, Leiden Univeristy, Leiden Netherlands (2013).

  38. A. Allais and J. McGreevy, How to construct a gravitating quantum electron star, Phys. Rev. D 88 (2013) 066006 [arXiv:1306.6075] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    Mariya V. Medvedyeva

  2. Institute for Theoretical Physics, J.W. Goethe-University, D-60438, Frankfurt am Main, Germany

    Elena Gubankova

  3. Instituut Lorentz, Delta-Institute for Theoretical Physics, Leiden University, Niels Bohrweg 2, 2300 RA, Leiden, The Netherlands

    Mihailo Čubrović, Koenraad Schalm & Jan Zaanen

Authors
  1. Mariya V. Medvedyeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena Gubankova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mihailo Čubrović
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Koenraad Schalm
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jan Zaanen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihailo Čubrović.

Additional information

ArXiv ePrint: 1302.5149

Rights and permissions

Reprints and permissions

About this article

Cite this article

Medvedyeva, M.V., Gubankova, E., Čubrović, M. et al. Quantum corrected phase diagram of holographic fermions. J. High Energ. Phys. 2013, 25 (2013). https://doi.org/10.1007/JHEP12(2013)025

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP12(2013)025

Keywords

Search

Navigation