Incipient Order in the t-J Model at High Temperatures

Physical Review Letters

Volumn 92, Issue 6, 2004, Pages 670021-670024

  Pryadko, Leonid P ^a   Kivelson, Steven A ^b   Zachar, Oron ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETIC MATERIALS; HAMILTONIANS; MAGNETIC SUSCEPTIBILITY; MAGNETIZATION; MATHEMATICAL MODELS; OXIDE SUPERCONDUCTORS; PEROVSKITE; SUPERCONDUCTIVITY;

FINITE SIZE EFFECTS; HIGH-TEMPERATURE SUPERCONDUCTIVITY;

HIGH TEMPERATURE SUPERCONDUCTORS;

EID: 1642286201     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. P. W. Andersen, Science 235, 1196 (1987); The Theory of Superconductivity in the High-Tc Cuprates (Princeton University Press, Princeton, New Jersey, 1997).
2. P. W. Andersen, Science 235, 1196 (1987); The Theory of Superconductivity in the High-Tc Cuprates (Princeton University Press, Princeton, New Jersey, 1997).
3. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60, 1057 (1988); Phys. Rev. B 39, 2344 (1989).
4. S. Chakravarty, B. I. Halperin, and D. R. Nelson, Phys. Rev. Lett. 60, 1057 (1988); Phys. Rev. B 39, 2344 (1989).
5. For recent reviews, see D. J. Scalapino and S. R. White, Found. Phys. 31, 27 (2001); E. W. Carlson et al., cond-mat/0206217 (unpublished), Sec. 11.
6. For recent reviews, see D. J. Scalapino and S. R. White, Found. Phys. 31, 27 (2001); E. W. Carlson et al., cond-mat/0206217 (unpublished), Sec. 11.
7. d-SC decreasing T found for the Hubbard model, see N. Bulut, D. J. Scalapino, and S. R. White, Phys. Rev. B 47, 6157 (1993); S. R. White et al., ibid. 39, 839 (1989), is not in conflict with our strong-coupling results.
8. d-SC decreasing T found for the Hubbard model, see N. Bulut, D. J. Scalapino, and S. R. White, Phys. Rev. B 47, 6157 (1993); S. R. White et al., ibid. 39, 839 (1989), is not in conflict with our strong-coupling results.
9. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
10. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
11. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
12. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
13. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
14. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
15. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
16. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
17. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
18. I. Affleck and J. B. Marston, Phys. Rev. B 37, 3774 (1988); J. Zaanen and O. Gunnarsson, ibid. 40, 7391 (1989); H. J. Schulz, Phys. Rev. Lett. 64, 1445 (1990); K. Machida, Physica C (Amsterdam) 158, 192 (1989); U. Löw et al., Phys. Rev. Lett 72, 1918 (1994); O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B 57, 1422 (1998); S.-C. Zhang, Science 275, 1089 (1997); S. A. Kivelson, E. Fradkin, and V. J. Emery, Nature (London) 393, 550 (1998); S. Chakravarty et al., Phys. Rev. B 63, 094503 (2001); S. Chakravarty, H.-Y. Kee, and C. Nayak, Int. J. Mod. Phys. B 15, 2901 (2001).
19. J. M. Tranquada et al., Nature (London) 375, 561 (1995).
20. For review of the status of experimental search for stripe and nematic order in the cuprates see S. A. Kivelson et al., Rev. Mod. Phys. 75, 1201 (2003).
21. H. A. Mook, P. Dai, and F. Dogan, Phys. Rev. B 64, 012502 (2001); H. A. Mook et al., ibid. 66, 144513 (2002).
22. H. A. Mook, P. Dai, and F. Dogan, Phys. Rev. B 64, 012502 (2001); H. A. Mook et al., ibid. 66, 144513 (2002).
23. Y. Ando et al., Phys. Rev. Lett 88, 137005 (2002).
24. Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1974), Vol. 3; J. G. A. Baker, Quantitative Theory of Critical Phenomena (Academic, San Diego, 1990).
25. Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1974), Vol. 3; J. G. A. Baker, Quantitative Theory of Critical Phenomena (Academic, San Diego, 1990).
26. R. R. P. Singh and R. L. Glenister, Phys. Rev. B 46, 11871 (1992); 46, 14313 (1992).
27. R. R. P. Singh and R. L. Glenister, Phys. Rev. B 46, 11871 (1992); 46, 14313 (1992).
28. (a) K. Kubo and M. Tada, Prog. Theor. Phys. 69, 1345 (1983);
29. (b) 71, 479 (1984).
30. W. O. Putikka, M. U. Luchini, and T. M. Rice, Phys. Rev. Lett. 68, 538 (1992); R. Hlubina et al., Phys. Rev. B 46, 11224 (1992).
31. W. O. Putikka, M. U. Luchini, and T. M. Rice, Phys. Rev. Lett. 68, 538 (1992); R. Hlubina et al., Phys. Rev. B 46, 11224 (1992).
32. D. F. B. ten Haaf el al., Phys. Rev. B 51, 353 (1995).
33. W. O. Putikka, M. U. Luchini, and R. R. P. Singh, Phys. Rev. Lett. 81, 2966 (1998); W. O. Putikka and M. U. Luchini, Phys. Rev. B 62, 1684 (2000).
34. W. O. Putikka, M. U. Luchini, and R. R. P. Singh, Phys. Rev. Lett. 81, 2966 (1998); W. O. Putikka and M. U. Luchini, Phys. Rev. B 62, 1684 (2000).
35. AF was previously computed to the same order in Ref. [11](a) and in A. Sokol, R. L. Glenister, and R. R. P. Singh, Phys. Rev. Lett. 72, 1549 (1994).
36. See additional plots at URL http://faculty.ucr.edu/~leonid/hts-all.pdf. The calculated series are available from the authors upon request.
37. The gauge-invariant d-DW susceptibility defined as the second derivative of the free energy with respect to staggered fluxes has a qualitatively similar behavior for x ≳ 11% (where it is positive).
38. S. Wolfram, Mathematica (Wolfram Research, Inc., Champaign, IL, 2001).
39. J. Oitmaa and E. Bornilla, Phys. Rev. B 53, 14 228 (1996).
40. M. Körner, M. Troyer, and W. O. Putikka, in Proceedings of the APS March Meeting 2003 (unpublished).