Zero temperature phase transitions in quantum Heisenberg ferromagnets

Annals of Physics

Volumn 251, Issue 1, 1996, Pages 76-122

  Sachdev, Subir ^a   Senthil, T ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030579032     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1006/aphy.1996.0108     Document Type: Article

References (55)

1. 1. E. C. Stoner, Proc. Roy. Soc. London A 154 (1936), 656.
2. 2. S. Sachdev, Z. Phys. B 94 (1994), 469.
3. 3. C. Pfleiderer, G. J. McMullan, and G. G. Lonzarich, Physica B 206 & 207 (1995), 847.
4. 4. J. A. Hertz, Phys. Rev. B 14 (1976), 525.
5. 5. A. J. Millis, Phys. Rev. B 48 (1993), 7183.
6. 6. S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51 (1995), 14874.
7. 7. P. C. Hohenberg and J. B. Swift, J. Phys. C 7 (1974), 4009.
8. 8. P. Fulde and I. Peschel, Adv. Phys. 21 (1972), 1; R. J. Birgeneau, J. Als-Nielsen and E. Bucher, Phys. Rev. Lett. 27 (1971), 1530.
9. 8. P. Fulde and I. Peschel, Adv. Phys. 21 (1972), 1; R. J. Birgeneau, J. Als-Nielsen and E. Bucher, Phys. Rev. Lett. 27 (1971), 1530.
10. 9. S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen, Science 264 (1994), 413.
11. 10. N. Furukawa, J. Phys. Soc. Jpn. 63 (1994), 3214; preprints cond-mat/9505011 and cond-mat/ 9505034; A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74 (1995), 5144.
12. 10. N. Furukawa, J. Phys. Soc. Jpn. 63 (1994), 3214; preprints cond-mat/9505011 and cond-mat/ 9505034; A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74 (1995), 5144.
13. 10. N. Furukawa, J. Phys. Soc. Jpn. 63 (1994), 3214; preprints cond-mat/9505011 and cond-mat/ 9505034; A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74 (1995), 5144.
14. 11. S. E. Barrett et al., Phys. Rev. Lett. 72 (1994), 1368; Phys. Rev. Lett. 74 (1995), 5112; R. Tycko et al., Science 268 (1995), 1460.
15. 11. S. E. Barrett et al., Phys. Rev. Lett. 72 (1994), 1368; Phys. Rev. Lett. 74 (1995), 5112; R. Tycko et al., Science 268 (1995), 1460.
16. 11. S. E. Barrett et al., Phys. Rev. Lett. 72 (1994), 1368; Phys. Rev. Lett. 74 (1995), 5112; R. Tycko et al., Science 268 (1995), 1460.
17. 12. D.-H. Lee and C. L. Kane, Phys. Rev. Lett. 64 (1990), 1313.
18. 13. H. A. Fertig, L. Brey, R. Cote, and A. H. MacDonald, Phys. Rev. B 50 (1994), 11018.
19. 14. S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Phys. Rev. B 47 (1993), 16419.
20. 15. M. Kasner and A. H. MacDonald, cond-mat/9510021.
21. 16. N. Read and S. Sachdev, Phys. Rev. Lett. 75 (1995), 3509.
22. 17. L. Brey, H. A. Fertig, R. Cote, and A. H. MacDonald, Phys. Rev. Lett. 75 (1995), 2562.
23. 18. N. Read, private communication.
24. 19. T. R. Kirkpatrick and D. Belitz, cond-mat/9601008.
25. 20. C. J. Hamer, J. B. Kogut, and L. Susskind, Phys. Rev. D 19 (1979), 3091.
26. 21. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60 (1988), 1057; Phys. Rev. B 39 (1989), 2344.
27. 21. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60 (1988), 1057; Phys. Rev. B 39 (1989), 2344.
28. 22. S. Sachdev and J. Ye, Phys. Rev. Lett. 69 (1992), 2411;
29. A. V. Chubukov and S. Sachdev, Phys. Rev. Lett. 71 (1993), 169;
30. A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49 (1994), 11919.
31. 23. J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett. 70 (1993), 4011; N. Read, S. Sachdev and J. Ye, Phys. Rev. B, 52 (1995), 384.
32. 23. J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett. 70 (1993), 4011; N. Read, S. Sachdev and J. Ye, Phys. Rev. B, 52 (1995), 384.
33. 24. A. J. Millis and H. Monien, Phys. Rev. Lett. 70 (1993), 2810; Phys. Rev. B 50 (1994), 16606; J. M. Tranquada, G. Shirane, B. Keimer, S. Shamoto, and M. Sato, Phys. Rev. B 40 (1989), 4503; A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72 (1994), 2777; A. W. Sandvik, A. V. Chubukov and S. Sachdev, Phys. Rev. B, 51 (1995), 16483.
34. 24. A. J. Millis and H. Monien, Phys. Rev. Lett. 70 (1993), 2810; Phys. Rev. B 50 (1994), 16606; J. M. Tranquada, G. Shirane, B. Keimer, S. Shamoto, and M. Sato, Phys. Rev. B 40 (1989), 4503; A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72 (1994), 2777; A. W. Sandvik, A. V. Chubukov and S. Sachdev, Phys. Rev. B, 51 (1995), 16483.
35. 24. A. J. Millis and H. Monien, Phys. Rev. Lett. 70 (1993), 2810; Phys. Rev. B 50 (1994), 16606; J. M. Tranquada, G. Shirane, B. Keimer, S. Shamoto, and M. Sato, Phys. Rev. B 40 (1989), 4503; A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72 (1994), 2777; A. W. Sandvik, A. V. Chubukov and S. Sachdev, Phys. Rev. B, 51 (1995), 16483.
36. 24. A. J. Millis and H. Monien, Phys. Rev. Lett. 70 (1993), 2810; Phys. Rev. B 50 (1994), 16606; J. M. Tranquada, G. Shirane, B. Keimer, S. Shamoto, and M. Sato, Phys. Rev. B 40 (1989), 4503; A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72 (1994), 2777; A. W. Sandvik, A. V. Chubukov and S. Sachdev, Phys. Rev. B, 51 (1995), 16483.
37. 24. A. J. Millis and H. Monien, Phys. Rev. Lett. 70 (1993), 2810; Phys. Rev. B 50 (1994), 16606; J. M. Tranquada, G. Shirane, B. Keimer, S. Shamoto, and M. Sato, Phys. Rev. B 40 (1989), 4503; A. W. Sandvik and D. J. Scalapino, Phys. Rev. Lett. 72 (1994), 2777; A. W. Sandvik, A. V. Chubukov and S. Sachdev, Phys. Rev. B, 51 (1995), 16483.
38. 25. M. P. A. Fisher, P. B. Weichmann, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40 (1989), 546.
39. 26. We could also have studied an analogous "quantum top model" to allow for the possibility of phases in which the spins are non-collinear but have no net ferromagnetic moment - the analog of the Néel phase in that model would have 3 spin-wave modes, all with ω ∼ k. The phases with a ferromagnetic moment in the quantum top model are quite similar to those being discussed here in the quantum rotor model, and we will therefore not enter into this complication in this paper.
40. 27. E. Brezin and J. Zinn-Justin, Phys. Rev. B 14 (1976), 3110. D. R. Nelson and R. A. Pelcovits, Phys. Rev. B 16 (1977), 2191.
41. 27. E. Brezin and J. Zinn-Justin, Phys. Rev. B 14 (1976), 3110. D. R. Nelson and R. A. Pelcovits, Phys. Rev. B 16 (1977), 2191.
42. 28. See e.g. D. Boyanovsky and J. L. Cardy, Phys. Rev. B 26 (1982), 154.
43. 29. S. Sachdev, T. Senthil, and R. Shankar, Phys. Rev. B 50 (1994), 258.
44. z(q, Ω) and take the limit Ω → 0 before taking q → 0.
45. 31. R. Shankar and N. Read, Nucl. Phys. B 336 (1990), 457.
46. 32. T. T. Wu and C. N. Yang, Nucl. Phys. B 107 (1976), 365.
47. 33. I. Affleck and F. D. M. Haldane, Phys. Rev. B 36 (1987), 5291.
48. 34. E. Witten, Comm. Math. Phys. 92 (1984), 455; V. G. Knizhnik and A. B. Zamalodchikov, Nucl. Phys. B 247 (1984), 83.
49. 34. E. Witten, Comm. Math. Phys. 92 (1984), 455; V. G. Knizhnik and A. B. Zamalodchikov, Nucl. Phys. B 247 (1984), 83.
50. R are also permitted. It may be necessary to include this term in the most general case.
51. 36. I. Affleck, in Les Houches XLIX, "Fields, Strings and Critical Phenomena" (E. Brezin and J. Zinn Justin, Eds.), p. 562, North Holland, Amsterdam, 1990.
52. 37. S. Sachdev in "Proceedings of the 19th IUPAP International Conference on Statistical Physics" (B.-L. Hao, Ed.), World Scientific, Singapore, in press; cond-mat/9508080.
53. 38. M. Aizenman and J. Wehr, Phys. Rev. Lett. 62 (1989), 2503; K. Hui and A. N. Berker, Phys. Rev. Lett. 62 (1989), 2507.
54. 38. M. Aizenman and J. Wehr, Phys. Rev. Lett. 62 (1989), 2503; K. Hui and A. N. Berker, Phys. Rev. Lett. 62 (1989), 2507.
55. 39. E. Brezin, J. C. Le Guillou and J. Zinn-Justin, in "Phase Transitions and Critical Phenomena" (C. Domb and M. S. Green, Eds.), Vol. 6, Academic Press, London, 1976.