Order and disorder in AKLT antiferromagnets in three dimensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 2, 2009, Pages

  Parameswaran, Siddharth A ^a   Sondhi, S L ^a   Arovas, Daniel P ^b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59249107224     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.024408     Document Type: Article

References (31)

1. P. W. Anderson, Mater. Res. Bull. 8, 153 (1973) 10.1016/0025-5408(73) 90167-0
2. P. Fazekas and P. W. Anderson, Philos. Mag. 30, 423 (1974). 10.1080/14786439808206568
3. More precisely the ideas of P. W. Anderson, Science 235, 1196 (1987). 10.1126/science.235.4793.1196
4. For a review, see S. Sachdev, in Low Dimensional Quantum Field Theories for Condensed Matter Physicists, edited by, Yu Lu,,, S. Lundqvist,, and, G. Morandi, (World Scientific, Singapore, 1995)
5. S. Sachdev, arXiv:cond-mat/9303014 (unpublished).
6. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987) 10.1103/PhysRevLett.59.799
7. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115, 477 (1988). 10.1007/BF01218021
8. Note that in Ref., the authors rule out the existence of Néel order for lattices of coordination number z=3.
9. J. T. Chayes, L. Chayes, and S. A. Kivelson, Commun. Math. Phys. 123, 53 (1989). 10.1007/BF01244017
10. K. S. Raman, R. Moessner, and S. L. Sondhi, Phys. Rev. B 72, 064413 (2005). 10.1103/PhysRevB.72.064413
11. D. J. Klein, J. Phys. A 15, 661 (1982). 10.1088/0305-4470/15/2/032
12. See also the closely related work on an XXZ model in d=3 of M. Hermele, M. P. A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004). 10.1103/PhysRevB.69.064404
13. D. P. Arovas, Phys. Rev. B 77, 104404 (2008). 10.1103/PhysRevB.77.104404
14. D. P. Arovas, A. Auerbach, and F. D. M. Haldane, Phys. Rev. Lett. 60, 531 (1988). 10.1103/PhysRevLett.60.531
15. T. Kennedy, E. H. Lieb, and H. Tasaki, J. Stat. Phys. 53, 383 (1988). 10.1007/BF01011563
16. A rigorous proof of this theorem for classical spin systems may be found in N. D. Mermin, J. Math. Phys. 8, 1061 (1967). While it does not address this particular interaction, the point of view we take is that if one chooses an ordered ground state and examines the effect of fluctuations, the result is that the long-wavelength modes destroy order, thereby precluding symmetry breaking; while we do not have an explicit proof of this statement, the physical motivations seem reasonable, and it is in this sense that we invoke the theorem. 10.1063/1.1705316
17. E. J. Neves and J. F. Perez, Phys. Lett. 114A, 331 (1986).
18. This approach was suggested to us by D. Huse; it is also described in Robert G. Brown and Mikael Ciftan, Phys. Rev. B 54, 15860 (1996). 10.1103/PhysRevB.54.15860
19. P. Peczak, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 43, 6087 (1991). 10.1103/PhysRevB.43.6087
20. System configurations were recorded after each lattice sweep, so 1 MCS is the natural unit of time along the Markov chains. A precise determination of the autocorrelation time was not performed, but plots of the error estimate were made for blocks of increasing length and initial position along the chain, which allowed us to check the convergence of physical quantities; the final block, consisting of the latter half of the chain, was used to perform averages in each thread.
21. K. Binder, Z. Phys. B: Condens. Matter 43, 119 (1981). 10.1007/BF01293604
22. M. E. Fisher, Rep. Prog. Phys. 30, 615 (1967). 10.1088/0034-4885/30/2/306
23. H. E. Stanley, Phys. Rev. 158, 546 (1967). 10.1103/PhysRev.158.546
24. R. Moessner and J. T. Chalker, Phys. Rev. Lett. 80, 2929 (1998) 10.1103/PhysRevLett.80.2929
25. R. Moessner and J. T. Chalker, Phys. Rev. B 58, 12049 (1998). 10.1103/PhysRevB.58.12049
26. S. V. Isakov, K. Gregor, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 93, 167204 (2004). 10.1103/PhysRevLett.93.167204
27. D. A. Huse and A. D. Rutenberg, Phys. Rev. B 45, 7536 (1992). 10.1103/PhysRevB.45.7536
28. R. J. Baxter, J. Math. Phys. 11, 784 (1970) 10.1063/1.1665210
29. the problem discussed here is the three-coloring problem on the 2d hexagonal lattice, which is equivalent to the model discussed in Ref..
30. S. A. Parameswaran, S. L. Sondhi, D. P. Arovas, and R. Moessner (unpublished).
31. S. A. Parameswaran, S. L. Sondhi, and D. P. Arovas (unpublished).