Skip to main content
SpringerLink
Log in

Interacting soluble Fermi systems in one dimension

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The Luttinger and the Mattis models are two exactly soluble models describing interacting fermions in one dimension. The recent, increasing interest in these models motivates our rigorous derivation of explicit general formulae for theirn-fields Schwinger functions. Such formulae are not known in the literature. We study also the asymptotic behaviour of Schwinger functions for large values of coordinates. The behaviour of some response functions of physical interest for small momenta is also obtained.

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. J. Luttinger:J. Math. Phys.,4, 1154 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Mattis:Physics,1, 183 (1964).

    Google Scholar 

  3. D. Mattis andE. Lieb:J. Math. Phys.,6, 304 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  4. S. Tomonaga:Ann. Phys. (N.Y.),3, 91 (1958).

    Article  ADS  Google Scholar 

  5. G. Benfatto andG. Gallavotti:J. Stat. Phys.,59, 541 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  6. G. Benfatto, G. Gallavotti andV. Mastropietro:Phys. Rev. B,45, 5468 (1992).

    Article  ADS  Google Scholar 

  7. G. Benfatto, G. Gallavotti, A. Procacci andB. Scoppola:Beta function and Schwinger functions for a many fermions system in one dimension. Anomaly of the Fermi surface, CARR Reports in Mathematical Physics 4/93, February 1993.

  8. F. Bonetto andV. Mastropietro:Renormalization theory for spinning one dimensional fermionic system, CARR Reports in Mathematical Physics 25/93, September 1993.

  9. V. Mastropietro:Nuovo Cimento B,108, 1095 (1993).

    Article  ADS  Google Scholar 

  10. W. Thirring:Ann. Phys. (N.Y.),3, 91 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  11. B. Klaiber:Lectures at Summer Institute for Theoretical Physics, University of Colorado, edited byA. Barut andW. Brittin (Gordon and Breach, New York, N.Y., 1968).

    Google Scholar 

  12. K. Osterwalder andR. Schrader:Commun. Math. Phys.,31, 83 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Luther andI. Peschel:Phys. Rev. B,9, 2911 (1974).

    Article  ADS  Google Scholar 

  14. I. E. Dzyaloshinskii andA. I. Larkin:Sov. Phys. JETP,38, 202 (1974).

    ADS  Google Scholar 

  15. J. Solyom:Adv. Phys.,28, 201 (1979).

    Article  ADS  Google Scholar 

  16. A. Theunmann:Phys. Rev. B,15, 4524 (1977).

    Article  ADS  Google Scholar 

  17. D. Aschroft andN. Mermin:Solid State Physics (Holt, Rinehart and Winston, New York, N.Y., 1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell’Università, 56100, Pisa, Italia

    V. Mastropietro

Authors
  1. V. Mastropietro
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mastropietro, V. Interacting soluble Fermi systems in one dimension. Nuovo Cim B 109, 1–23 (1994). https://doi.org/10.1007/BF02723725

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02723725

PACS 03.65

Search

Navigation