Mechanisms for spin supersolidity in S= 1 2 spin-dimer antiferromagnets

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 18, 2008, Pages

  Picon, J D ^a,b   Albuquerque, A F ^a,c   Schmidt, K P ^d   Laflorencie, N ^e   Troyer, M ^a   Mila, F ^b  

^a ETH ZURICH   (Switzerland)

^b EPFL   (Switzerland)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

^d TU DORTMUND UNIVERSITY   (Germany)

^e UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 57349095425     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.184418     Document Type: Article

References (54)

1. T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Nat. Phys. 4, 198 (2008). 10.1038/nphys893
2. E. Kim and M. H. W. Chan, Nature (London) 427, 225 (2004). 10.1038/nature02220
3. E. Kim and M. H. W. Chan, Science 305, 1941 (2004). 10.1126/science. 1101501
4. S. Sasaki, R. Ishiguro, F. Caupin, H. J. Maris, and S. Balibar, Science 313, 1098 (2006). 10.1126/science.1130879
5. J.-P. Bouchaud and G. Biroli, arXiv:0710.3087 (unpublished).
6. L. Pollet, M. Boninsegni, A. B. Kuklov, N. V. Prokof'ev, B. V. Svistunov, and M. Troyer, Phys. Rev. Lett. 98, 135301 (2007). 10.1103/PhysRevLett.98. 135301
7. L. Pollet, M. Boninsegni, A. B. Kuklov, N. V. Prokof'ev, B. V. Svistunov, and M. Troyer, Phys. Rev. Lett. 101, 097202 (2008). 10.1103/PhysRevLett.101. 097202
8. G. G. Batrouni and R. T. Scalettar, Phys. Rev. Lett. 84, 1599 (2000). 10.1103/PhysRevLett.84.1599
9. G. Schmid, S. Todo, M. Troyer, and A. Dorneich, Phys. Rev. Lett. 88, 167208 (2002). 10.1103/PhysRevLett.88.167208
10. P. Sengupta, L. P. Pryadko, F. Alet, M. Troyer, and G. Schmid, Phys. Rev. Lett. 94, 207202 (2005). 10.1103/PhysRevLett.94.207202
11. S. Wessel and M. Troyer, Phys. Rev. Lett. 95, 127205 (2005). 10.1103/PhysRevLett.95.127205
12. D. Heidarian and K. Damle, Phys. Rev. Lett. 95, 127206 (2005). 10.1103/PhysRevLett.95.127206
13. R. G. Melko, A. Paramekanti, A. A. Burkov, A. Vishwanath, D. N. Sheng, and L. Balents, Phys. Rev. Lett. 95, 127207 (2005). 10.1103/PhysRevLett.95. 127207
14. M. Boninsegni and N. V. Prokof'ev, Phys. Rev. Lett. 95, 237204 (2005). 10.1103/PhysRevLett.95.237204
15. G. G. Batrouni, F. Hébert, and R. T. Scalettar, Phys. Rev. Lett. 97, 087209 (2006). 10.1103/PhysRevLett.97.087209
16. Y. C. Chen, R. G. Melko, S. Wessel, and Y. J. Kao, Phys. Rev. B 77, 014524 (2008). 10.1103/PhysRevB.77.014524
17. K. P. Schmidt, J. Dorier, A. M. Läuchli, and F. Mila, Phys. Rev. Lett. 100, 090401 (2008). 10.1103/PhysRevLett.100.090401
18. K.-K. Ng and T. K. Lee, Phys. Rev. Lett. 97, 127204 (2006). 10.1103/PhysRevLett.97.127204
19. N. Laflorencie and F. Mila, Phys. Rev. Lett. 99, 027202 (2007). 10.1103/PhysRevLett.99.027202
20. P. Sengupta and C. D. Batista, Phys. Rev. Lett. 98, 227201 (2007). 10.1103/PhysRevLett.98.227201
21. P. Sengupta and C. D. Batista, Phys. Rev. Lett. 99, 217205 (2007). 10.1103/PhysRevLett.99.217205
22. Plotted QMC results for the CBS structure factor S (π,π) both for the spin-dimer model of Eq. 1 (Fig. 2) and for the minimal effective model [Eqs. 9 10] (shown in Fig. 8) have been renormalized so that a perfectly ordered CBS plateau would lead to S (π,π) =1, as within our MF approach, Eq. 5. In this way, we can see that S (π,π) is reduced to ∼60-70% of its classical value when quantum fluctuations are taken into account.
23. K. Totsuka, Phys. Rev. B 57, 3454 (1998). 10.1103/PhysRevB.57.3454
24. F. Mila, Eur. Phys. J. B 6, 201 (1998). 10.1007/s100510050542
25. To second order in J/ J, the processes appearing in Figs. 3 3 have the same amplitude. This is not the case for the effective Hamiltonian obtained from CORE; see Table 1.
26. F. Wegner, Ann. Phys. 77, 3 (1994).
27. S. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993). 10.1103/PhysRevD.48.5863
28. S. D. Glazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994). 10.1103/PhysRevD.49.4214
29. C. Knetter, K. P. Schmidt, M. Grüninger, and G. S. Uhrig, Phys. Rev. Lett. 87, 167204 (2001). 10.1103/PhysRevLett.87.167204
30. J. Stein, J. Stat. Phys. 88, 487 (1997). 10.1007/BF02508481
31. A. Mielke, Eur. Phys. J. B 5, 605 (1998). 10.1007/s100510050485
32. G. S. Uhrig and B. Normand, Phys. Rev. B 58, R14705 (1998). 10.1103/PhysRevB.58.R14705
33. C. Knetter and G. S. Uhrig, Eur. Phys. J. B 13, 209 (2000). 10.1007/s100510050026
34. F. Mila and K. P. Schmidt, Springer Ser. Solid-State Sci. (to be published).
35. J. Dorier, K. P. Schmidt, and F. Mila, arXiv:0806.3406, Phys. Rev. Lett. (to be published).
36. C. Knetter, K. P. Schmidt, and G. S. Uhrig, J. Phys. A 36, 7889 (2003). 10.1088/0305-4470/36/29/302
37. C. J. Morningstar and M. Weinstein, Phys. Rev. Lett. 73, 1873 (1994). 10.1103/PhysRevLett.73.1873
38. C. J. Morningstar and M. Weinstein, Phys. Rev. D 54, 4131 (1996). 10.1103/PhysRevD.54.4131
39. A. Abendschein and S. Capponi, Phys. Rev. B 76, 064413 (2007). 10.1103/PhysRevB.76.064413
40. E. Altman and A. Auerbach, Phys. Rev. B 65, 104508 (2002). 10.1103/PhysRevB.65.104508
41. S. Capponi, Theor. Chem. Acc. 116, 524 (2006). 10.1007/s00214-006-0090-8
42. S. Capponi, A. Läuchli, and M. Mambrini, Phys. Rev. B 70, 104424 (2004). 10.1103/PhysRevB.70.104424
43. We remark that it is nontrivial to quantitatively relate the condensate density ρ0 [density of particles occupying the lowest energy mode, obtained within our MF procedure from Eq. 4] and the superfluid stiffness ρs [that measures the system's phase coherence and is obtained in terms of winding numbers in the QMC simulations, Eq. 11]. For a discussion of how ρ0, ρs and the superfluid density are related, the reader is referred to Refs.; in the present case, this issue is further complicated by the presence of correlated hopping terms in the effective Hamiltonian Eq. 9. However, we stress that the comparison between different results for the location of the SS phase suffices for concluding on the mechanism for spin supersolidity in the model [Eq. 1], the goal of the present study.
44. It is interesting to note that the effective uncorrelated hoppings for holes with range- 21/2 (NNN) and -2 (third-neighbor) have zero amplitude within the CORE approach and therefore cannot account for supersolidity in the spin-dimer model, Eq. 1. Accordingly, they are not present in the minimal model, Eq. 9, which therefore does not suffer from the sign problem.
45. By reducing t 1C from the starting value 0.145 and keeping all the other couplings appearing in Eq. 9 unchanged, CBS and SS already appear for t 1C ∼0.14.
46. A MF analysis for the enlarged minimal model including, besides terms appearing in Eq. 9, the correlated hopping terms with amplitudes s 3C and s 5C [Eq. 4], reveals an enlarged SS region (compared with the one obtained for the full effective model). This suggests that the terms with amplitudes s 3C and s 5C play a role in stabilizing SS and the fact that they are not explicitly included in the minimal model [Eq. 9] might explain the shrunk SS region in our QMC results.
47. K. P. Schmidt, J. Dorier, A. Läuchli, and F. Mila, Phys. Rev. B 74, 174508 (2006). 10.1103/PhysRevB.74.174508
48. F. Alet, S. Wessel, and M. Troyer, Phys. Rev. E 71, 036706 (2005). 10.1103/PhysRevE.71.036706
49. F. Alet, J. Phys. Soc. Jpn. Suppl. 74, 30 (2005).
50. A. W. Sandvik, Phys. Rev. B 59, R14157 (1999). 10.1103/PhysRevB.59.R14157
51. O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002). 10.1103/PhysRevE.66.046701
52. T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16, 569 (1956). 10.1143/PTP.16.569
53. M. E. Fisher, M. N. Barber, and D. Jasnow, Phys. Rev. A 8, 1111 (1973). 10.1103/PhysRevA.8.1111
54. K. Bernardet, G. G. Batrouni, J.-L. Meunier, G. Schmid, M. Troyer, and A. Dorneich, Phys. Rev. B 65, 104519 (2002). 10.1103/PhysRevB.65.104519