Luttinger theorem and imbalanced Fermi systems

Regular Article

Abstract

The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a “conserving” approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any “Φ-derivable” approximation, and illustrate it in particular for the self-consistent t-matrix approximation.

Keywords

Solid State and Materials 

References

  1. 1.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, in Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963), Chap. 4Google Scholar
  2. 2.
    P. Nozières, Theory of Interacting Fermi Systems (Benjamin, New York, 1964)Google Scholar
  3. 3.
    G. Rickayzen, in Green’s Functions and Condensed Matter (Academic Press, London, 1980), Chap. 6Google Scholar
  4. 4.
    J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    J.M. Luttinger, Phys. Rev. 119, 1153 (1960)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    A. Praz, J. Feldman, H. Knörrer, E. Trubowitz, Europhys. Lett. 72, 49 (2005)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    G. Baym, L.P. Kadanoff, Phys. Rev. 124, 287 (1961)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    G. Baym, Phys. Rev. 127, 1391 (1962)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Ortloff, M. Balzer, M. Potthoff, Eur. Phys. J. B 58, 37 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    G.B. Partridge, W. Li, R.I. Kamar, Y. Liao, R.G. Hulet, Science 311, 503 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    A. Perali, P. Pieri, G.C. Strinati, C. Castellani, Phys. Rev. B 66, 024510 (2002)ADSCrossRefGoogle Scholar
  14. 14.
    P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)ADSCrossRefGoogle Scholar
  15. 15.
    X.-J. Liu, H. Hu, Europhys. Lett. 75, 364 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    M.M. Parish, F.M. Marchetti, A. Lamacraft, B.D. Simons, Nat. Phys. 3, 124 (2007)CrossRefGoogle Scholar
  17. 17.
    T. Kashimura, R. Watanabe, Y. Ohashi, J. Low Temp. Phys. 171, 355 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    A. Tartari, Ph.D. Thesis, University of Camerino, 2011Google Scholar
  19. 19.
    M. Urban, P. Schuck, Phys. Rev. A 90, 023632 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    A. Perali, F. Palestini, P. Pieri, G.C. Strinati, J.T. Stewart, J.P. Gaebler, T.E. Drake, D.S. Jin, Phys. Rev. Lett. 106, 060402 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    T. Kashimura, R. Watanabe, Y. Ohashi, Phys. Rev. A 86, 043622 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    A.L. Fetter, J.D. Walecka, in Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971), Chap. 7Google Scholar
  24. 24.
    G.C. Strinati, in The BCS-BEC Crossover and the Unitary Fermi Gas, edited by W. Zwerger, Lecture Notes in Physics (Springer-Verlag, Berlin, Heidelberg, 2012), Vol. 836, pp. 99–125Google Scholar
  25. 25.
    R. Combescot, S. Giraud, Phys. Rev. Lett. 101, 050404 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Pierbiagio Pieri
    • 1
    • 2
  • Giancarlo Calvanese Strinati
    • 1
    • 2
  1. 1.School of Science and Technology, Physics Division, Università di CamerinoCamerino (MC)Italy
  2. 2.INFN, Sezione di PerugiaPerugia (PG)Italy

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