Testing for Z 2 topological order in variational wave functions for spin liquids

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 9, 2005, Pages

  Paramekanti, Arun ^a   Randeria, Mohit ^b,c,d   Trivedi, Nandini ^b,c,d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^c University of Illinois at Urbana Champaign   (United States)

^d OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; HIGH TEMPERATURE; INSULATOR ELEMENT; MATHEMATICAL ANALYSIS; PHYSICS; SUPERCONDUCTOR; THERMODYNAMICS;

EID: 20344382495     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.094421     Document Type: Article

References (41)

1. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
2. N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991).
3. X. G. Wen, Phys. Rev. B 44, 2664 (1991)
4. and Cargese Lectures (1990, unpublished).
5. T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000).
6. L. Balents, M. P. A. Fisher, and S. M. Girvin, Phys. Rev. B 65, 224412 (2002).
7. O. I. Motrunich and T. Senthil, Phys. Rev. Lett. 89, 277004 (2002).
8. P. W. Anderson, Science 235, 1196 (1987).
9. A. Paramekanti, M. Randeria, and N. Trivedi, Phys. Rev. Lett. 87, 217002 (2001);
10. Phys. Rev. B 70, 054504 (2004);
11. M. Randeria, A. Paramekanti, and N. Trivedi, Phys. Rev. B ibid. 69, 214517 (2004).
12. N. Read and B. Chakraborty, Phys. Rev. B 40, 7133 (1989).
13. D. A. Ivanov and T. Senthil, Phys. Rev. B 66, 115111 (2002).
14. G. Misguich, C. Lhuillier, B. Bernu, and C. Waldtmann, Phys. Rev. B 60, 1064 (1999);
15. G. Misguich, C. Lhuillier, M. Mambrini, and P. Sindzingre, Eur. Phys. J. B 26, 167 (2002).
16. H. Morita, S. Watanabe, and M. Imada, J. Phys. Soc. Jpn. 71, 2109 (2002); M. Imada, T. Masuzaki, and S. Watanabe, condmat/0307022.
17. F. F. Assaad, Phys. Rev. B 71, 075103 (2005).
18. A. Paramekanti and A. Vishwanath, Phys. Rev. B 70, 245118 (2004).
19. var used in Ref. 8.
20. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
21. N. E. Bonesteel, Phys. Rev. B 40, 8954 (1989).
22. L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 60, 1654 (1999).
23. We have checked that the particular projected wave function we use has no long-range magnetic or valence bond order and thus describes a translationally invariant spin liquid.
24. We have checked that local spin correlations are identical in the thermodynamic limit for states with and without a vison. These states are thus locally identical and differ only in their global (topological) properties.
25. I. Affleck and E. Lieb, Lett. Math. Phys. 12, 57 (1986);
26. I. Affleck, Phys. Rev. B 37, 5186 (1988).
27. See M. M. Hastings, Phys. Rev. B 69, 104431 (2004), for a recent extension to two dimensions.
28. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (N.Y.) 16, 407 (1961).
29. S. Sorella, L. Capriotti, F. Becca, and A. Parola, Phys. Rev. Lett. 91, 257005 (2003). This paper discusses a particular chiral spin liquid state which has a broken translational symmetry on oddleg ladders consistent with the LSM theorem (Ref. 21), but such that the corresponding dimer order parameter vanishes in the limit of infinite number of chains. Nevertheless, in this twodimensional limit, there is a nonzero value for the chiral order parameter which is a local spin operator.
30. See M. Randeria, in Bose Einstein Condensation, edited by A. Griffin, D. Snoke, and S. Stringari (Cambridge University Press, Cambridge, 1995).
31. I. Affleck, Z. Zou, T. Hsu, and P. W. Anderson, Phys. Rev. B 38, 745 (1988).
32. This result was earlier obtained by Wen (Ref. 3) by analyzing the stability of mean field solutions for spin models. See T. Li and H.-Y. Yanf, cond-mat/0405034, for a different approach.
33. 2 gauge theory, see J. Kogut, Rev. Mod. Phys. 51, 659 (1979).
34. R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2002).
35. xy); the results are consistent with those presented here.
36. This value of Δ was chosen as it is the value which gives the minimum energy for the Hubbard model at half-filling. For more details on this, see Sec. IX and Ref. 8.
37. The factor of 2 is included in the asymptotic decay definition since we are looking at overlap of states with two visons in different directions.
38. C. Gros, Phys. Rev. B 38, 931 (1988).
39. T. Senthil and M. P. A. Fisher, Phys. Rev. Lett. 86, 292 (2001).
40. D. A. Bonn, J. C. Wynn, B. C. Gardner, Y. J. Lin, R. Liang, W. N. Hardy, J. R. Kirtley, and K. A. Moler, Nature (London) 414, 887 (2001).
41. S. Sorella, Phys. Rev. B 64, 024512 (2001).