Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 2, 2009, Pages

  Isaev, L ^a   Ortiz, G ^a   Dukelsky, J ^b  

^a INDIANA UNIVERSITY   (United States)

^b INSTITUTO DE ESTRUCTURA DE LA MATERIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59249098039     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.024409     Document Type: Article

References (39)

1. P. Carretta, R. Melzi, N. Papinutto, and P. Millet, Phys. Rev. Lett. 88, 047601 (2002) 10.1103/PhysRevLett.88.047601
2. A. Bombardi, J. Rodriguez-Carvajal, S. Di Matteo, F. de Bergevin, L. Paolasini, P. Carretta, P. Millet and R. Caciuffo, Phys. Rev. Lett. 93, 027202 (2004). 10.1103/PhysRevLett.93.027202
3. P. Carretta, N. Papinutto, C. B. Azzoni, M. C. Mozzati, E. Pavarini, S. Gonthier, and P. Millet, Phys. Rev. B 66, 094420 (2002). 10.1103/PhysRevB.66. 094420
4. R. Nath, A. A. Tsirlin, H. Rosner, and C. Geibel, Phys. Rev. B 78, 064422 (2008). 10.1103/PhysRevB.78.064422
5. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
6. G. Misguich and C. Lhuillier, in Frustrated Spin Systems, edited by, H. T. Diep, (World Scientific, Singapore, 2004).
7. L. Capriotti and S. Sorella, Phys. Rev. Lett. 84, 3173 (2000). 10.1103/PhysRevLett.84.3173
8. L. Capriotti, F. Becca, A. Parola, and S. Sorella, Phys. Rev. Lett. 87, 097201 (2001). 10.1103/PhysRevLett.87.097201
9. M. S. L. du Croo de Jongh, J. M. J. van Leeuwen, and W. van Saarloos, Phys. Rev. B 62, 14844 (2000). 10.1103/PhysRevB.62.14844
10. R. Darradi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Krueger, and J. Richter, Phys. Rev. B 78, 214415 (2008). 10.1103/PhysRevB.78.214415
11. R. R. P. Singh, Z. Weihong, C. J. Hamer, and J. Oitmaa, Phys. Rev. B 60, 7278 (1999). 10.1103/PhysRevB.60.7278
12. K. Takano, Y. Kito, Y. Ono, and K. Sano, Phys. Rev. Lett. 91, 197202 (2003). 10.1103/PhysRevLett.91.197202
13. V. N. Kotov, J. Oitmaa, O. P. Sushkov, and Z. Weihong, Phys. Rev. B 60, 14613 (1999). 10.1103/PhysRevB.60.14613
14. V. Lante and A. Parola, Phys. Rev. B 73, 094427 (2006). 10.1103/PhysRevB.73.094427
15. N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991). 10.1103/PhysRevLett.66.1773
16. T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Phys. Rev. B 70, 144407 (2004). 10.1103/PhysRevB.70.144407
17. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Statistical Physics, Parts 1 and 2 (Butterworth-Heinemann, New York, 1999)
18. K. G. Wilson and J. Kogut, Phys. Rep., Phys. Lett. 12, 75 (1974). 10.1016/0370-1573(74)90023-4
19. E. Manousakis, Rev. Mod. Phys. 63, 1 (1991). 10.1103/RevModPhys.63.1
20. That the translational symmetry is broken in the Néel phase is easy to see if one assumes broken spin SU(2) symmetry. Then, due to the principle of weakening of correlations, the staggered correlation function satisfies lim | i-j | →∞ (-1) i-j 〈 Siz Sjz 〉 = (-1) i-j 〈 Siz 〉 〈 Sjz 〉, which can be constant only if 〈 Siz 〉 depends on i.
21. J. Sirker, Z. Weihong, O. P. Sushkov, and J. Oitmaa, Phys. Rev. B 73, 184420 (2006). 10.1103/PhysRevB.73.184420
22. A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007). 10.1103/PhysRevLett. 98.227202
23. C. D. Batista and S. A. Trugman, Phys. Rev. Lett. 93, 217202 (2004). 10.1103/PhysRevLett.93.217202
24. G. Ortiz and C. D. Batista, Phys. Rev. B 67, 134301 (2003) 10.1103/PhysRevB.67.134301
25. Condensed Matter Theories, edited by, M. de Llano,,, C. Fiolhais,, and, J. da Providencia, (Nova Science, New York, 2003), Vol. 18.
26. M. van den Bossche, F.-C. Zhang, and F. Mila, Eur. Phys. J. B 17, 367 (2000). 10.1007/PL00011085
27. E. Altman and A. Auerbach, Phys. Rev. B 65, 104508 (2002). 10.1103/PhysRevB.65.104508
28. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1957).
29. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, 1994).
30. N. Trivedi and D. M. Ceperley, Phys. Rev. B 40, 2737 (1989). 10.1103/PhysRevB.40.2737
31. A. L. Fetter, Ann. Phys. (N.Y.) 70, 67 (1972). 10.1016/0003-4916(72) 90330-2
32. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. 10, 1388 (1969). 10.1063/1.1664978
33. K. Okamoto and K. Nomura, Phys. Lett. A 169, 433 (1992). 10.1016/0375-9601(92)90823-5
34. E. H. Lieb, T. D. Schultz, and D. C. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961). 10.1016/0003-4916(61)90115-4
35. M. B. Hastings, Phys. Rev. B 69, 104431 (2004). 10.1103/PhysRevB.69. 104431
36. M. E. Fisher, Phys. Rev. 124, 1664 (1961). 10.1103/PhysRev.124.1664
37. F. Kruger and S. Scheidl, Europhys. Lett. 74, 896 (2006). 10.1209/epl/i2006-10039-3
38. S. R. White, Phys. Rev. Lett. 77, 3633 (1996). 10.1103/PhysRevLett.77. 3633
39. J. P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, 1986).