First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy

Physical Review B - Condensed Matter and Materials Physics

Volumn 86, Issue 15, 2012, Pages

  Chubukov, Andrey V ^a   Maslov, Dmitrii L ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867812816     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.86.155136     Document Type: Article

References (58)

1. M. Fowler and R. Prange, Physics (NY) 1, 315 (1965).
2. S. Engelsberg and G. Simpson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.2.1657 2, 1657 (1970);
3. S. Engelsberg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.18.966 18, 966 (1978).
4. G. W. Martin, D. L. Maslov, and M. Y. Reizer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.241309 68, 241309 (R) (2003).
5. Y. Adamov, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.045426 73, 045426 (2006). (Pubitemid 43276680)
6. A. Wasserman and M. Springford, Adv. Phys. ADPHAH 0001-8732 10.1080/00018739600101547 45, 471 (1996).
7. Ar. Abanov, A. V. Chubukov, and J. Schmalian, Adv. Phys. ADPHAH 0001-8732 10.1080/0001873021000057123 52, 119 (2003).
8. A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.245123 71, 245123 (2005). (Pubitemid 41702913)
9. A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.13 68, 13 (1996).
10. G. M. Eliashberg, Zh. Eksp. Teor. Fiz. 42, 1658 (1962)
11. G. M. Eliashberg, [Sov. Phys. JETP 15, 1151 (1962)];
12. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, 2nd ed. (Pergamon, Oxford, 1965), Chap.19.6.
13. J. Rech, C. Pépin, and A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.195126 74, 195126 (2006). (Pubitemid 44838406)
14. B. L. Altshuler, L. B. Ioffe, and A. J. Millis, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.14048 50, 14048 (1994);
15. Y. B. Kim, A. Furusaki, X-G. Wen, and P. A. Lee, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.17917 50, 17917 (1994);
16. Chetan Nayak and Frank Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90477-4 417, 359 (1994);
17. Chetan Nayak and Frank Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90158-9 430, 534 (1994);
18. Joseph Polchinski, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94) 90449-9 422, 617 (1994);
19. S. Chakravarty, R.E. Norton, and O. F. Syljuasen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.1423 74, 1423 (1995).
20. S. Gangadharaiah, D. L. Maslov, A. V. Chubukov, and L. I. Glazman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.156407 94, 156407 (2005); (Pubitemid 40620384)
21. A. V. Chubukov, D. L. Maslov, S. Gangadharaiah, and L. I. Glazman, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.205112 71, 205112 (2005). (Pubitemid 43285172)
22. S.-S. Lee, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.165102 80, 165102 (2009).
23. M. A. Metlitski and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.075127 82, 075127 (2010).
24. D. L. Maslov and A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.045110 81, 045110 (2010).
25. M. A. Metlitski and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.075128 82, 075128 (2010);
26. M. A. Metlitski and S. Sachdev, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/10/105007 12, 105007 (2010).
27. D. F. Mross, J. McGreevy, H. Liu, and T. Senthil, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.045121 82, 045121 (2010).
28. T. Senthil, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.035103 78, 035103 (2008).
29. D. L. Maslov and A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.155137 86, 155137 (2012).
30. J. M. Luttinger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.121.942 121, 942 (1961).
31. C. Hodges, H. Smith, and J. W. Wilkins, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.4.302 4, 302 (1971).
32. A. V. Chaplik, Zh. Eksp. Teor. Fiz. 60, 1845 (1971)
33. A. V. Chaplik, [Sov. Phys. JETP 33, 997 (1971)].
34. G. F. Giuliani and J. J. Quinn, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.26.4421 26, 4421 (1982).
35. L. Zheng and S. Das Sarma, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.53.9964 53, 9964 (1996).
36. D. Menashe and B. Laikhtman, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.54.11561 54, 11561 (1996).
37. T. Jungwirth and A. H. MacDonald, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.53.7403 53, 7403 (1996).
38. M. Reizer and J. W. Wilkins, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.55.R7363 55, R7363 (1997).
39. B. N. Narozhny, G. Zala, and I. L. Aleiner, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.180202 65, 180202 (2002).
40. A. V. Chubukov and D. L. Maslov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.155113 68, 155113 (2003).
41. Z. Qian and G. Vignale, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.075112 71, 075112 (2005). (Pubitemid 40410816)
42. I. L. Aleiner and K. B. Efetov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.075102 74, 075102 (2006); (Pubitemid 44182256)
43. H. Meier, C. Pépin, and K. B. Efetov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.205131 84, 205131 (2011).
44. A. V. Chubukov, D. L. Maslov, and A. J. Millis, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.045128 73, 045128 (2006). (Pubitemid 43270678)
45. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.579 77, 579 (2005). (Pubitemid 41491331)
46. D. L. Maslov, A. V. Chubukov, and R. Saha, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.220402 74, 220402 (R) (2006); (Pubitemid 44927310)
47. D. L. Maslov and A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.075112 79, 075112 (2009).
48. L. Dell Anna and W. Metzner, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.045127 73, 045127 (2006); (Pubitemid 43276659)
49. H. Yamase, V. Oganesyan, and W. Metzner, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.035114 72, 035114 (2005); (Pubitemid 41506686)
50. M. Zacharias, P. Wölfle, and M. Garst, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.165116 80, 165116 (2009);
51. M. Garst and A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.235105 81, 235105 (2010);
52. E. Fradkin, S. A. Kivelson, M. J. Lawler, J. P. Eisenstein, and A. P. Mackenzie, Annu. Rev. Condens. Matter Phys. 1947-5454 10.1146/annurev- conmatphys-070909-103925 1, 153 (2010).
53. A. V. Chubukov, Y.-B. Kim, and S. S. Lee (unpublished).
54. A. J. Millis, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.7183 48, 7183 (1993).
55. See, e.g., C. M. Varma, Z. Nussinov, and W. van Saarloos, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00060-6 361, 267 (2002), and references therein.
56. E. Abrahams and C. M. Varma, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.100118797 97, 5714 (2000). (Pubitemid 30367463)
57. Ar. Abanov and A. Chubukov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.255702 93, 255702 (2004). (Pubitemid 40141847)
58. E. Weisstein, Quantum Calculus: MathWorld, A Wolfram Web Resource, edited by, V. Kac, and, P. Cheung, (Springer, Berlin, 2001).