Skip to main content
SpringerLink
Log in

A holographic flat band

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

Abstract

We describe a novel implementation of non-relativistic fermions in AdS/CFT by imposing Lorentz violating boundary terms for a Dirac spinor in AdS4. The dual boundary theory is scale invariant and exhibits a number of interesting properties, including a dispersionless flat band of gapless excitations.

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. A. Mielke, Ferromagnetism in the Hubbard model on line graphs and further considerations, J. Phys. A 24 (1991) 3311.

    ADS  MathSciNet  Google Scholar 

  2. A. Mielke, Exact ground states for the Hubbard model on the Kagome lattice, J. Phys. A 25 (1992) 4335.

    ADS  MathSciNet  Google Scholar 

  3. H. Tasaki, Ferromagnetism in the Hubbard model with degenerate single-electron ground states, Phys. Rev. Lett. 69 (1992) 1608.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. M. Imada and M. Kohno, Superconductivity from flat dispersion designed in doped Mott insulators, Phys. Rev. Lett. Letters 84 (2000) 143 [arXiv:cond-mat/9911185].

    Article  ADS  Google Scholar 

  5. N.B. Kopnin, T.T. Heikkilä and G.E. Volovik, High-temperature surface superconductivity in topological flat-band systems, Phys. Rev. B 83 (2011) 220503 [arXiv:1103.2033].

    ADS  Google Scholar 

  6. H. Katsura, I. Maruyama, A. Tanaka and H. Tasaki, Ferromagnetism in the Hubbard model with topological/non-topological flat bands, EPL (Europhys. Lett.) 915 (2010) 57007 [arXiv:0907.4564].

    Article  ADS  Google Scholar 

  7. D. Green, L. Santos and C. Chamon, Isolated flat bands and spin-1 conical bands in two-dimensional lattices, Phys. Rev. B 82 (2010) 075104 [arXiv:1004.0708].

    ADS  Google Scholar 

  8. E. Tang, J.-W. Mei and X.-G. Wen, High-temperature fractional quantum Hall states, Phys. Rev. Lett. 106 (2011) 236802 [arXiv:1012.2930].

    Article  ADS  Google Scholar 

  9. K. Sun, Z. Gu, H. Katsura and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106 (2011) 236803 [arXiv:1012.5864].

    Article  ADS  Google Scholar 

  10. C. Wu, D. Bergman, L. Balents and S. Das Sarma, Flat bands and Wigner crystallization in the honeycomb optical lattice, Phys. Rev. Lett. 99 (2007) 070401 [arXiv:cond-mat/0701788].

    Article  ADS  Google Scholar 

  11. E. Suárez Morell, J.D. Correa, P. Vargas, M. Pacheco and Z. Barticevic, Flat bands in slightly twisted bilayer graphene: tight-binding calculations, Phys. Rev. B 82 (2010) 121407 [arXiv:1012.4320].

    ADS  Google Scholar 

  12. T.T. Heikkilä, N. Kopnin and G. Volovik, Flat bands in topological media, JETP Lett. 94 (2011) 233 [arXiv:1012.0905] [INSPIRE].

    Article  ADS  Google Scholar 

  13. S.-S. Lee, A non-Fermi liquid from a charged black hole: a critical Fermi ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [INSPIRE].

    ADS  Google Scholar 

  14. 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 

  15. M. Cubrovic, 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  Google Scholar 

  16. 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 

  17. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, From black holes to strange metals, arXiv:1003.1728 [INSPIRE].

  18. T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Holographic non-Fermi liquid fixed points, arXiv:1101.0597 [INSPIRE].

  19. S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  20. D. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  21. K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  22. 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  MATH  MathSciNet  ADS  Google Scholar 

  23. M. Henneaux, Boundary terms in the AdS/CFT correspondence for spinor fields, hep-th/9902137 [INSPIRE].

  24. P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys B 556 (1999) 89 [hep-th/9905104] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  26. E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].

  27. M. Berkooz, A. Sever and A. Shomer, ’Double trace’ deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  28. A. Allais, Double-trace deformations, holography and the c-conjecture, JHEP 11 (2010) 040 [arXiv:1007.2047] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  29. J.N. Laia and D. Tong, Flowing between fermionic fixed points, arXiv:1108.2216 [INSPIRE].

  30. M. Porrati and L. Girardello, The three dimensional dual of 4d chirality, JHEP 11 (2009) 114 [arXiv:0908.3487] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  31. M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  32. W. Mueck and K. Viswanathan, Conformal field theory correlators from classical field theory on Anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].

    ADS  Google Scholar 

  33. S.A. Hartnoll, D.M. Hofman and A. Tavanfar, Holographically smeared Fermi surface: quantum oscillations and Luttinger count in electron stars, Europhys. Lett. 95 (2011) 31002 [arXiv:1011.2502] [INSPIRE].

    Article  ADS  Google Scholar 

  34. 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  Google Scholar 

  35. N. Iqbal, H. Liu and M. Mezei, Semi-local quantum liquids, arXiv:1105.4621 [INSPIRE].

  36. E.W. Leaver, Quasinormal modes of Reissner-Nordstrom black holes, Phys. Rev. D 41 (1990) 2986 [INSPIRE].

  37. F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K.

    João N. Laia & David Tong

Authors
  1. João N. Laia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Tong.

Additional information

ArXiv ePrint: 1108.1381

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laia, J.N., Tong, D. A holographic flat band. J. High Energ. Phys. 2011, 125 (2011). https://doi.org/10.1007/JHEP11(2011)125

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2011)125

Keywords

Search

Navigation