Skip to main content

The Renormalization Group Approach – From Fermi Liquids to Quantum Dots

  • Chapter
  • First Online:
  • 895 Accesses

Part of the book series: Lecture Notes in Physics ((LNP,volume 667))

Abstract

Imagine that you have some problem in the form of a partition function

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. M. E. Fisher Critical Phenomena, F. W. J. Hahne, Editor, Lecture Notes Number 186, Springer-Verlag, Berlin, (1983). These notes are from the Engelbrecht Summer School of 1983!

    Google Scholar 

  2. R. Shankar (1991) Physica A177 530

    Google Scholar 

  3. R. Shankar, Physica A177, 530 (1991); R.Shankar, Rev. Mod. Phys. 66, 129 (1994).

    Article  Google Scholar 

  4. L. D. Landau, Sov. Phys. JETP 3, 920 (1956); Sov. Phys. JETP 5, 101 (1957).

    Google Scholar 

  5. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover Publications, New York, 1963.

    Google Scholar 

  6. D. J. Gross and A. Neveu, Phys. Rev. D10, 3235 (1974).

    Google Scholar 

  7. P. Polchinski In: TASI Elementary Particle Physics, ed by J. Polchinski and J.Harvey (World Scientific, 1992.)

    Google Scholar 

  8. T. Guhr A. Müller-Groeling H. A. Weidenmüller (1998) Phys. Rep. 299 189 Occurrence Handle10.1016/S0370-1573(97)00088-4 Occurrence Handle1:CAS:528:DyaK1cXivVKntb8%3D

    Article  CAS  Google Scholar 

  9. Y. Alhassid (2000) Rev. Mod. Phys. 72 895 Occurrence Handle10.1103/RevModPhys.72.895 Occurrence Handle1:CAS:528:DC%2BD3cXovVGrsLg%3D

    Article  CAS  Google Scholar 

  10. For recent reviews, see, T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299, 189 (1998); Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000); A. D. Mirlin, Phys. Rep. 326, 259 (2000).

    Article  CAS  Google Scholar 

  11. M. L. Mehta (1991) Random Matrices Academic Press San Diego

    Google Scholar 

  12. K. B. Efetov (1983) Adv. Phys. 32 53

    Google Scholar 

  13. M. L. Mehta, Random Matrices, Academic Press, San Diego, 1991. K. B. Efetov, Adv. Phys. 32, 53 (1983); B. L. Al’tshuler and B. I. Shklovskii, Sov. Phys. JETP 64, 127 (1986).

    Google Scholar 

  14. I. L. Aleiner, P. W. Brouwer, and L. I. Glazman, Phys. Rep. 358, 309 (2002), and references therein; Y. Oreg, P. W. Brouwer, X. Waintal, and B. I. Halperin, cond-mat/0109541, “Spin, spin-orbit, and electron-electron interactions in mesoscopic systems”.

    Article  CAS  Google Scholar 

  15. R. A. Jalabert, A. D. Stone, and Y. Alhassid, Phys. Rev. Lett. 68, 3468 (1992).

    Article  PubMed  Google Scholar 

  16. A. M. Chang H. U. Baranger L. N. Pfeiffer K. W. West T. Y. Chang (1996) Phys. Rev. Lett. 76 1695 Occurrence Handle10.1103/PhysRevLett.76.1695 Occurrence Handle1:CAS:528:DyaK28XhtlGntLw%3D Occurrence Handle10060494

    Article  CAS  PubMed  Google Scholar 

  17. A. M. Chang, H. U. Baranger, L. N. Pfeiffer, K. W. West, and T. Y. Chang, Phys. Rev. Lett. 76, 1695 (1996); J. A. Folk, S. R. Patel, S. F. Godjin, A. G. Huibers, S. M. Cronenwett, and C. M. Marcus, Phys. Rev. Lett. 76, 1699 (1996).

    Article  CAS  PubMed  Google Scholar 

  18. S. R. Patel, D. R. Stewart, C. M. Marcus, M. Gokcedag, Y. Alhassid, A. D. Stone, C. I. Dururoz, and J. S. Harris, Phys. Rev. Lett. 81, 5900 (1998).

    Article  CAS  Google Scholar 

  19. D. V. Averin K. K. Likharev (1991) B. L. Altshuler P. A. Lee R. Webb (Eds) Mesoscopic Phenomena in Solids Elsevier Amsterdam

    Google Scholar 

  20. D. V. Averin and K. K. Likharev, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. Webb (Elsevier, Amsterdam, 1991); C. W. J. Beenakker, Phys. Rev. B44, 1646 (1991).

    Google Scholar 

  21. A. V. Andreev A. Kamenev (1998) Phys. Rev. Lett. 81 3199 Occurrence Handle10.1103/PhysRevLett.81.3199 Occurrence Handle1:CAS:528:DyaK1cXmsFyhs7Y%3D

    Article  CAS  Google Scholar 

  22. P. W. Brouwer Y. Oreg B. I. Halperin (1999) Phys. Rev. 60 R13977 Occurrence Handle10.1103/PhysRevB.60.R13977 Occurrence Handle1:CAS:528:DyaK1MXnsF2jtr0%3D

    Article  CAS  Google Scholar 

  23. A. V. Andreev and A. Kamenev, Phys. Rev. Lett. 81, 3199 (1998), P. W. Brouwer, Y. Oreg, and B. I. Halperin, Phys. Rev. 60, R13977 (1999), H. U. Baranger, D. Ullmo, and L. I. Glazman, Phys. Rev. 61, R2425 (2000).

    Article  CAS  Google Scholar 

  24. I. L. Kurland, I. L. Aleiner, and B. L. Al’tshuler, Phys. Rev. 62, 14886 (2000).

    Article  CAS  Google Scholar 

  25. O. Prus A. Auerbach Y. Aloni U. Sivan R. Berkovits (1996) Phys. Rev. 54 R14289 Occurrence Handle10.1103/PhysRevB.54.R14289 Occurrence Handle1:CAS:528:DyaK28XnsVSks70%3D

    Article  CAS  Google Scholar 

  26. O. Prus, A. Auerbach, Y. Aloni, U. Sivan, and R. Berkovits, Phys. Rev. 54, R14289 (1996), R. Berkovits, Phys. Rev. Lett. 81, 2128 (1998), A. Cohen, K. Richter, and R. Berkovits, Phys. Rev. 60, 2536 (1999), P. N. Walker, G. Montambaux, and Y. Gefen, ibid, 2541 (1999), S. Levit and D. Orgad, Phys. Rev. 60, 5549 (1999), D. Ullmo and H. U. Baranger, Phys. Rev. 64, 245324 (2001), V. Belinicher, E. Ginossar, and S. Levit, cond-mat/0109005, Y. Alhassid and S. Malhotra, cond-mat/0202453.

    Google Scholar 

  27. U. Sivan et al. (1996) Phys. Rev. Lett. 77 1123 Occurrence Handle10.1103/PhysRevLett.77.1123 Occurrence Handle1:CAS:528:DyaK28XltFWlt70%3D Occurrence Handle10062996

    Article  CAS  PubMed  Google Scholar 

  28. U. Sivan et al, Phys. Rev. Lett. 77, 1123 (1996); S. R. Patel et al, Phys. Rev. Lett. 80, 4522 (1998).

    Article  CAS  Google Scholar 

  29. F. Simmel et al. (1999) Phys. Rev. 59 10441 Occurrence Handle10.1103/PhysRevB.59.R10441

    Article  Google Scholar 

  30. F. Simmel et al, Phys. Rev. 59, 10441 (1999); D. Abusch-Magder et al, Physica E 6, 382 (2000).

    CAS  Google Scholar 

  31. Y. M. Blanter A. D. Mirlin B. A. Muzykantskii (1997) Phys. Rev. Lett. 78 2449 Occurrence Handle10.1103/PhysRevLett.78.2449 Occurrence Handle1:CAS:528:DyaK2sXitVynt78%3D

    Article  CAS  Google Scholar 

  32. Y. M. Blanter, A. D. Mirlin, and B. A. Muzykantskii, Phys. Rev. Lett. 78, 2449 (1997), R. O. Vallejos, C. H. Lewenkopf, and E. R. Mucciolo, Phys. Rev. Lett. 81, 677 (1998).

    Article  CAS  Google Scholar 

  33. S. Adam, P. W. Brouwer, J. P. Sethna, and X. Waintal, cond-mat/0203002.

    Google Scholar 

  34. J. B. French S. S. M. Wong (1970) Phys. Lett. 33B 447

    Google Scholar 

  35. O. Bohigas J. Flores (1971) Phys. Lett. 34B 261

    Google Scholar 

  36. Y. Alhassid Ph. Jacquod A. Wobst (2000) Phys. Rev. B61 13357

    Google Scholar 

  37. J. B. French and S. S. M. Wong, Phys. Lett. 33B, 447 (1970), “O. Bohigas and J. Flores, Phys. Lett. 34B, 261 (1971), Y. Alhassid, Ph. Jacquod, and A. Wobst, Phys. Rev. 61, 13357 (2000), Physica E 9, 393 (2001), Y. Alhassid and A. Wobst, Phys. Rev. 65, 041304 (2002).

    Google Scholar 

  38. A. Tscherich and K. B. Efetov, Phys. Rev. 62, 2042 (2000).

    Google Scholar 

  39. G. Murthy and H. Mathur, Phys. Rev. Lett. 89, 126804 (2002).

    Article  PubMed  Google Scholar 

  40. G. Murthy and R. Shankar, Phys. Rev. Lett. 90, 066801 (2003).

    Article  PubMed  Google Scholar 

  41. G Murthy, R. Shankar, Damir Herman, and Harsh Mathur, cond-mat 0306529, Phys. Rev. 69, 075321, (2004).

    Article  Google Scholar 

  42. A. M. Finkel’shtein (1983) Sov. Phys. JETP 57 97

    Google Scholar 

  43. A. M. Finkel’shtein, Sov. Phys. JETP 57, 97 (1983); C. Castellani, C. Di Castro, P. A. Lee, and M. Ma, Phys. Rev. 30, 527 (1984).

    CAS  Google Scholar 

  44. For a review of the theory, see, D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994).

    Article  CAS  Google Scholar 

  45. D. Belitz T. R. Kirkpatrick (1996) Phys. Rev. 53 14364 Occurrence Handle10.1103/PhysRevB.53.14364

    Article  Google Scholar 

  46. D. Belitz and T. R. Kirkpatrick, Phys. Rev. 53, 14364 (1996); C. de C. Chamon and E. Mucciolo, Phys. Rev. Lett. 85, 5607 (2000); C. Nayak and X. Yang, cond-mat/0302503.

    CAS  Google Scholar 

  47. I. I. Pomeranchuk, Sov. Phys. JETP 8, 361 (1958).

    Google Scholar 

  48. C. M. Varma, Phys. Rev. Lett. 83, 3538 (1999).

    Article  CAS  Google Scholar 

  49. V. Oganesyan, S. A. Kivelson, and E. Fradkin, Phys. Rev. 64, 195109 (2001).

    Article  Google Scholar 

  50. S. Chakravarty B. I. Halperin D. R. Nelson (1988) Phys. Rev. Lett. 60 1057 Occurrence Handle10.1103/PhysRevLett.60.1057 Occurrence Handle10037930

    Article  PubMed  Google Scholar 

  51. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60, 1057 (1988); Phys. Rev. 39, 2344 (1989); For a detailed treatment of the generality of the phenomenon, see, S. Sachdev, Quantum Phase Transitions, Cambridge University Press, Cambridge 1999.

    Google Scholar 

  52. Shaffique Adam, Piet W. Brouwer, and Prashant Sharma Phys. Rev. B 68, 241311 (2003).

    Google Scholar 

  53. G. Murthy, Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dotscond-mat-0406029.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

W. Dieter Heiss

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Shankar, R. The Renormalization Group Approach – From Fermi Liquids to Quantum Dots. In: Dieter Heiss, W. (eds) Quantum Dots: a Doorway to Nanoscale Physics. Lecture Notes in Physics, vol 667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11358817_1

Download citation

Publish with us

Policies and ethics