Exact renormalization group flow equations for nonrelativistic fermions: Scaling toward the Fermi surface

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 15, 2001, Pages

  Kopietz, Peter ^a   Busche, Tom ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CORRELATION FUNCTION; DENSITY; RATING SCALE; REACTION ANALYSIS; REDUCTION; SPECTRAL SENSITIVITY;

EID: 0035887411     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.155101     Document Type: Article

References (53)

1. D. Zanchi and H.J. Schulz, Phys. Rev. B 54, 9509 (1996);
2. D. ZanchiH.J. SchulzZ. Phys. B: Condens. Matter 103, 339 (1997);
3. D. ZanchiH.J. SchulzPhys. Rev. B 61, 13 609 (2000).
4. C. J. Halboth, Ph.D. thesis, Shaker-Verlag, Aachen, 1999.
5. C.J. Halboth and W. Metzner, Phys. Rev. B 61, 4364 (2000);
6. C.J. HalbothW. MetznerPhys. Rev. Lett. 85, 5162 (2000).
7. C. Honerkamp, Ph.D. thesis, ETH Zürich, 2000.
8. C. Honerkamp, M. Salmhofer, N. Furukawa, and T.M. Rice, Phys. Rev. B 63, 045114 (2001);
9. M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. 105, 1 (2001);
10. C. Honerkamp, cond-mat/0103172 (unpublished).
11. F.J. Wegner and A. Houghton, Phys. Rev. A 8, 401 (1973).
12. K.G. Wilson, Phys. Rev. Lett. 26, 548 (1972);
13. K.G. Wilson and J.G. Kogut, Phys. Rep., Phys. Lett. 12C, 75 (1974).
14. S. K. Ma, Modern Theory of Critical Phenomena (Benjamin/Cummings, Reading, MA, 1976).
15. For a recent review, see M.E. Fisher, Rev. Mod. Phys. 70, 653 (1998).
16. T.L. Bell and K.G. Wilson, Phys. Rev. B 74, 3935 (1974).
17. J.F. Nicoll, T.S. Chang, and H.E. Stanley, Phys. Lett. A 57, 7 (1976);
18. Phys. Lett. AJ.F. Nicoll and T.S. Chang, 62, 287 (1977);
19. T.S. Chang, D.D. Vvedensky, and J.F. Nicoll, Phys. Rep. 217, 279 (1992).
20. J. Polchinski, Nucl. Phys. B 231, 269 (1984).
21. C. Wetterich, Phys. Lett. B 301, 90 (1993).
22. T.R. Morris, Int. J. Mod. Phys. A 9, 2411 (1994).
23. M. Salmhofer, Renormalization (Springer, Berlin, 1998).
24. C. Bagnuls and C. Bervillier, Phys. Rep. 348, 91 (2001).
25. P. Kopietz, Nucl. Phys. B 595, 493 (2001).
26. R. Shankar, Rev. Mod. Phys. 66, 129 (1994).
27. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1989); M. Le Ballac, Quantum and Statistical Field Theory (Clarendon Press, Oxford, 1991).
28. J.M. Luttinger, Phys. Rev. 119, 1153 (1960).
29. If (Formula presented) lies outside a closed Fermi surface (as shown in Fig. 11), then the mapping (Formula presented) defined by (Formula presented) yields a unique (Formula presented) for each (Formula presented). On the other hand, if (Formula presented) lies inside a closed Fermi surface, then (Formula presented) may have more than one solution (Formula presented) In this case we choose the solution which minimizes (Formula presented).
30. K.B. Blagoev and K.S. Bedell, Phys. Rev. Lett. 79, 1106 (1997);
31. Phys. Rev. Lett.M. Yamanaka, M. Oshikawa, and I. Affleck, 79, 1110 (1997).
32. J. W. Negele and H. Orland, Quantum Many-Particle Systems, (Addison-Wesley, Redwood City, CA, 1988).
33. W. Metzner, C. Castellani, and C. Di Castro, Adv. Phys. 47, 317 (1998).
34. J. Feldman, M. Salmhofer, and E. Trubowitz, J. Stat. Phys. 84, 1209 (1996);
35. J. FeldmanM. SalmhoferE. TrubowitzCommun. Pure Appl. Math. 51, 1133 (1998).
36. U. Ellwanger, Z. Phys. C 62, 503 (1994).
37. We introduce (Formula presented) because then the bosonic version of the exact flow equations of Sec. II can be simply obtained by replacing (Formula presented).
38. Although we use a different notation, our Eq. (2.16) is equivalent to the flow equation for the Legendre effective action given in Refs. 4 and 5. We have adopted the same notation as Ref. 16 to emphasize the analogy with (Formula presented) theory.
39. G.Y. Chitov and D. Sénéchal, Phys. Rev. B 52, 13 487 (1995);
40. Phys. Rev. BG.Y. ChitovD. Sénéchal 57, 1444 (1998);
41. Phys. Rev. BN. Dupuis and G.Y. Chitov, 54, 3040 (1996).
42. N. Dupuis, Eur. Phys. J. B 3, 315 (1998);
43. N. DupuisInt. J. Mod. Phys. B 14, 379 (2000).
44. C. Honerkamp and M. Salmhofer, cond-mat/0105218 (unpublished).
45. K. Louis, J.V. Alvarez, and C. Gros, cond-mat/0103009 (unpublished).
46. P.W. Anderson, Phys. Rev. Lett. 71, 1220 (1993).
47. J. Comellas, Nucl. Phys. B 509, 602 (1998).
48. J. Sólyom, Adv. Phys. 28, 201 (1979).
49. P. Carta, Phys. Rev. B 62, 10 687 (2000).
50. J. Voit, Rep. Prog. Phys. 57, 977 (1994).
51. T. Busche and P. Kopietz (unpublished).
52. B. Binz, D. Baeriswyl, and B. Douçot, cond-mat/0104424 (unpublished).
53. A. Ferraz, cond-mat/0104576 (unpublished).