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Interacting Many-Body Systems

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The Flow Equation Approach to Many-Particle Systems

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 217))

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Abstract

In the previous chapters we have discussed various applications of the flow equation method for simple Hamiltonians. These applications were meant to familiarize the reader with the method in a pedagogical way. However, the flow equation method is designed as an analytical tool for solving nonperturbative interacting many-body problems that are much more complicated than the Hamiltonians in these previous examples. In order to look at such problems, we first need to introduce another ingredient for realistic flow equation applications, namely the concept of normal-ordering. Then we will discuss three examples of flow equation solutions that highlight different aspects of such many-body applications: the Kondo model as a fermionic impurity model in Sect. 4.2, the spin–boson model as a bosonic impurity model in Sect. 4.3, and Fermi liquid theory in Sect. 4.4.

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References

  1. G.C. Wick, Phys. Rev. 80, 268 (1950)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. F.G. Scholtz, B.H. Bartlett, and H.B. Geyer, Phys. Rev. Lett. 91, 080602 (2003)

    Article  ADS  Google Scholar 

  3. J.N. Kriel, A.Y. Morozov, and F.G. Scholtz, J. Phys. A 38, 205 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. E. Körding and F. Wegner, J. Phys. A 39, 1231 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  5. K.W. Becker, A. Hübsch, and T. Sommer, Phys. Rev. B 66, 235115 (2002)

    Article  ADS  Google Scholar 

  6. A. Hübsch and K.W. Becker, Phys. Rev. B 71, 155116 (2005)

    Article  ADS  Google Scholar 

  7. W. Hofstetter and S. Kehrein, Phys. Rev. B 63, 140402 (2001)

    Article  ADS  Google Scholar 

  8. S. Kehrein, Phys. Rev. Lett. 95, 056602 (2005)

    Article  ADS  Google Scholar 

  9. A.C. Hewson: The Kondo Problem to Heavy Fermions, 1st edn (Cambridge University Press, Cambridge 1993)

    Book  Google Scholar 

  10. D. Withoff and E. Fradkin, Phys. Rev. Lett. 64, 1835 (1990)

    Article  ADS  Google Scholar 

  11. M. Vojta and R. Bulla, Phys. Rev. B 65, 014511 (2002)

    Article  ADS  Google Scholar 

  12. L. Fritz and M. Vojta, Phys. Rev. B 70, 214427 (2004)

    Article  ADS  Google Scholar 

  13. A.J. Leggett, S. Chakravarty, A.T. Dorsey, M.P.A. Fisher, A. Garg, and W. Zwerger, Rev. Mov. Phys. 59, 1 (1987)

    Article  ADS  Google Scholar 

  14. U. Weiss: Quantum Dissipative Systems, 2nd edn (World Scientific, Singapore 1999)

    Book  MATH  Google Scholar 

  15. S. Kehrein and A. Mielke, Ann. Phys. (Leipzig) 6, 90 (1997)

    MATH  MathSciNet  ADS  Google Scholar 

  16. S. Kehrein and A. Mielke, J. Stat. Phys. 90, 889 (1998)

    Article  MATH  ADS  Google Scholar 

  17. T. Stauber and A. Mielke, J. Phys. A 36, 2707 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. T. Stauber, Phys. Rev. B 68, 125102 (2003)

    Article  ADS  Google Scholar 

  19. S. Kleff, S. Kehrein, and J. von Delft, Phys. Rev. B 70, 014516 (2004)

    Article  ADS  Google Scholar 

  20. F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994)

    MATH  ADS  Google Scholar 

  21. A. Kabel and F. Wegner, Z. Phys. B 103, 555 (1997)

    Article  ADS  Google Scholar 

  22. T. Stauber, Phys. Rev. B 69, 113315 (2004)

    Article  ADS  Google Scholar 

  23. P. Nozières: Theory of Interacting Fermi Systems, 1st edn (Benjamin, New York 1964)

    MATH  Google Scholar 

  24. R. Shankar, Rev. Mod. Phys. 66, 129 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  25. I. Grote, E. Körding and F. Wegner, J. Low Temp. Phys. 126, 1385 (2002)

    Article  Google Scholar 

  26. V. Hankevych, I. Grote, and F. Wegner, Phys. Rev. B 66, 094516 (2002)

    Article  ADS  Google Scholar 

  27. V. Hankevych and F. Wegner, Acta Phys. Pol. B 34, 497 (2003); Erratum 34, 1591 (2003)

    Google Scholar 

  28. V. Hankevych and F. Wegner, Eur. Phys. J. B 31, 497 (2003)

    Article  Google Scholar 

  29. M. Salmhofer, Comm. Math. Phys. 194, 249 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. C. Honerkamp and M. Salmhofer, Phys. Rev. B 64, 184516 (2001)

    Article  ADS  Google Scholar 

  31. S. Andergassen, T. Enss, V. Meden, W. Metzner, U. Schollwöck, and K. Schönhammer, Phys. Rev. B 70, 075102 (2004)

    Article  ADS  Google Scholar 

  32. C.J. Halboth and W. Metzner, Phys. Rev. B 61, 7364 (2000)

    Article  ADS  Google Scholar 

  33. C.J. Halboth and W. Metzner, Phys. Rev. Lett. 85, 5162 (2000)

    Article  ADS  Google Scholar 

  34. H. Fröhlich, Proc. Roy. Soc. A 215, 291 (1952)

    Article  MATH  ADS  Google Scholar 

  35. A. Mielke, Eur. Phys. J. B 5, 605 (1998)

    Article  ADS  Google Scholar 

  36. D.Z. Anderson, R.W. Brockett, and N. Nuttall, Phys. Rev. Lett. 82, 1418 (1999)

    Article  ADS  Google Scholar 

  37. P. Lenz and F. Wegner, Nucl. Phys. B[FS] 482, 693 (1996)

    Article  ADS  Google Scholar 

  38. A. Hübsch and K.W. Becker, Eur. Phys. J. 33, 391 (2003)

    ADS  Google Scholar 

  39. A. Mielke, Europhys. Lett. 40, 195 (1997)

    Article  ADS  Google Scholar 

  40. A. Mielke, Ann. Phys. (Leipzig) 6, 215 (1997)

    MATH  MathSciNet  ADS  Google Scholar 

  41. P.B. Allen and B. Mitrović, Theory of Superconducting Tc.. In: Solid State Physics, vol 37, ed by H. Ehrenreich, F. Seitz, D. Turnbull (Academic Press, New York 1982), pp 1–92

    Google Scholar 

  42. E.W. Carlson, V.J. Emery, S.A. Kivelson, and D. Orgad, Concepts in High Temperature Superconductivity. In: The Physics of Superconductors, vol 2, ed by K.H. Bennemann, J.B. Ketterson (Springer, Berlin Heidelberg New York 2004), pp 275–452

    Google Scholar 

  43. M. Ragwitz and F. Wegner, Eur. Phys. J. B 8, 9 (1999)

    Article  ADS  Google Scholar 

  44. J.R. Schrieffer and P.A. Wolff, Phys. Rev. 149, 491 (1966)

    Article  ADS  Google Scholar 

  45. S. Kehrein and A. Mielke, Ann. Phys. (NY) 252, 1 (1996)

    Article  ADS  Google Scholar 

  46. C. Raas, A. Bühler, and G.S. Uhrig, Eur. Phys. J. B 21, 369 (2001)

    Article  ADS  Google Scholar 

  47. A. Reischl, E. Müller–Hartmann, and G.S. Uhrig, Phys. Rev. B 70, 245124 (2004)

    Article  ADS  Google Scholar 

  48. T. Domanski, Phys. Rev. A 68, 013603 (2003)

    Article  ADS  Google Scholar 

  49. T. Domanski and J. Ranninger, Phys. Rev. B 63, 134505 (2001)

    Article  ADS  Google Scholar 

  50. T. Domanski and J. Ranninger, Phys. Rev. Lett. 91 255301 (2003)

    Article  ADS  Google Scholar 

  51. C. Knetter and G.S. Uhrig, Eur. Phys. J. B 13, 209 (2000)

    Article  ADS  Google Scholar 

  52. C.P. Heidbrink and G.S. Uhrig, Eur. Phys. J. B 30, 443 (2002)

    Article  ADS  Google Scholar 

  53. C. Knetter, K.P. Schmitt, and G.S. Uhrig, Eur. Phys. J. B 36, 525 (2004)

    Article  ADS  Google Scholar 

  54. K.P. Schmidt, H. Monien, and G.S. Uhrig, Phys. Rev. B 67, 184413 (2003)

    Article  ADS  Google Scholar 

  55. K.P. Schmidt and G.S. Uhrig, Phys. Rev. Lett. 90, 227204 (2003)

    Article  ADS  Google Scholar 

  56. K.P. Schmidt, Ch. Knetter, and G.S. Uhrig, Phys. Rev. B 69, 104417 (2004)

    Article  ADS  Google Scholar 

  57. Ch. Knetter and G.S. Uhrig, Phys. Rev. Lett. 92, 027204 (2004)

    Article  ADS  Google Scholar 

  58. J. Stein, J. Stat. Phys. 88, 487 (1997)

    Article  MATH  ADS  Google Scholar 

  59. J. Stein, Eur. Phys. J. B 5, 193 (1998)

    Article  ADS  Google Scholar 

  60. S. Dusuel and J. Vidal, Phys. Rev. Lett. 93, 237204 (2004)

    Article  ADS  Google Scholar 

  61. S. Dusuel and J. Vidal, Phys. Rev. B 71, 224420 (2005)

    Article  ADS  Google Scholar 

  62. S. Dusuel and J. Vidal, Phys. Rev. A 71, 060304 (2005)

    Article  ADS  Google Scholar 

  63. W. Brenig, Phys. Rev. B 67, 064402 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  64. A.B. Bylev and H.J. Pirner, Phys. Lett. B 428, 329 (1998)

    Article  ADS  Google Scholar 

  65. D. Cremers and A. Mielke, Physica D 126, 123 (1999)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Ludwig-Maximilians-Universität München Fakultät für Physik, Theresienstr. 37, München, 80333, Germany

    Stefan Kehrein

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  1. Stefan Kehrein
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© 2006 Springer

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Kehrein, S. (2006). Interacting Many-Body Systems. In: The Flow Equation Approach to Many-Particle Systems. Springer Tracts in Modern Physics, vol 217. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34068-8_4

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