Bipartite Rokhsar-Kivelson points and Cantor deconfinement

Physical Review B - Condensed Matter and Materials Physics

Volumn 69, Issue 22, 2004, Pages

  Fradkin, Eduardo ^a   Huse, David A ^b   Moessner, R ^c   Oganesyan, V ^b   Sondhi, S L ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CANTOR DECONFINEMENT; COMPACT U(1) GAUGE THEORY; CRYSTAL; GROUND STATE; MAGNETIC FIELD; MAGNETIC TRANSITION; MAGNETISM; QUANTUM DIMER MODEL; QUANTUM MECHANICS; QUANTUM VERTEX MODEL; ROKHSAR KIVELSON POINT; SPINON; THEORETICAL MODEL; VALENCE BOND CRYSTAL;

EID: 37649026499     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.69.224415     Document Type: Article

References (36)

1. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
2. See R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2002), for an introduction to quantum dimer models from the present perspective.
3. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).
4. G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. 89, 137202 (2002).
5. R. Moessner and S. L. Sondhi, Phys. Rev. B 68, 054405 (2003).
6. X.-G. Wen, Phys. Rev. B 44, 2664 (1991); T. H. Hansson, V. Oganesyan, and S. L. Sondhi, cond-mat/0404327 (unpublished).
7. X.-G. Wen, Phys. Rev. B 44, 2664 (1991); T. H. Hansson, V. Oganesyan, and S. L. Sondhi, cond-mat/0404327 (unpublished).
8. S. Sachdev, Phys. Rev. B 40, 5204 (1989).
9. L. B. Ioffe and I. E. Larkin, Phys. Rev. B 40, 6941 (1989).
10. E. Fradkin and S. A. Kivelson, Mod. Phys. Lett. B 4, 225 (1990).
11. L. S. Levitov, Phys. Rev. Lett. 64, 92 (1990).
12. P. W. Leung, K. C. Chiu, and K. J. Runge, Phys. Rev. B 54, 12938 (1996).
13. R. Moessner, S. L. Sondhi, and P. Chandra, Phys. Rev. B 64, 144416 (2001).
14. D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003).
15. R. Moessner and S. L. Sondhi, Phys. Rev. B 68, 184512 (2003).
16. M. Hermele, M. P. A. Fisher, and L. Balents, Phys. Rev. B 69, 064404 (2004).
17. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science 303, 1490 (2004).
18. N. Read and S. Sachdev, Nucl. Phys. B 316, 609 (1989); Phys. Rev. Lett. 62, 1694 (1989); Phys. Rev. B 42, 4568 (1990).
19. N. Read and S. Sachdev, Nucl. Phys. B 316, 609 (1989); Phys. Rev. Lett. 62, 1694 (1989); Phys. Rev. B 42, 4568 (1990).
20. N. Read and S. Sachdev, Nucl. Phys. B 316, 609 (1989); Phys. Rev. Lett. 62, 1694 (1989); Phys. Rev. B 42, 4568 (1990).
21. See E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, Redwood City, 1991), Chap. 6, where there is a detailed discussion of the winding numbers in the quantum dimer model on the square lattice as a gauge theory, its connection with quantum roughening (or height) models, and of the deconfining character of the RK point.
22. W. Thurston, Am. Math. Monthly 97, 757 (1990).
23. R. Youngblood, J. D. Axe, and B. M. McCoy, Phys. Rev. B 21, 5212 (1980).
24. E. Fradkin and S. A. Kivelson, Mod. Phys. Lett. B 4, 225 (1990).
25. These flows were studied previously in a different, classical, context by G. Grinstein, Phys. Rev. B 23, 4615 (1981).
26. The d=2 classical to d=3 quantum connection is present also at the level of the wave function of the quantum model which is given by the statistical Gibbs weight of the 2D classical Gaussian model. Thus, at an RK quantum critical point, these systems have scale invariant ground state wave functions. This and other aspects of this problem are discussed in E. Ardonne, P. Fendley, and E. Fradkin, Ann. Phys. (N.Y.) 310, 493 (2004).
27. A. M. Polyakov, Nucl. Phys. B 120, 429 (1977).
28. C. L. Henley, J. Stat. Phys. 89, 483 (1997); cond-mat/0311345 (unpublished).
29. S. Aubry, in Solitons in Condensed Matter Physics, edited by A. Bishop and T. Schneider (Springer, Berlin, 1978), p. 264.
30. P. Chaikin and T. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995), Chap. 10 contains a fine introduction to this set of ideas. The important ideas on the connection between the Kolmogorov-Arnold-Moser (KAM) theorem in classical dynamics and the existence of the weak locking regime that underlie our assertions in this section are discussed in E. H. Fradkin, O. Hernandez, B. A. Huberman, and R. Pandit, Nucl. Phys. B 215, 137 (1983).
31. P. Chaikin and T. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 1995), Chap. 10 contains a fine introduction to this set of ideas. The important ideas on the connection between the Kolmogorov-Arnold-Moser (KAM) theorem in classical dynamics and the existence of the weak locking regime that underlie our assertions in this section are discussed in E. H. Fradkin, O. Hernandez, B. A. Huberman, and R. Pandit, Nucl. Phys. B 215, 137 (1983).
32. A. Vishwanath, L. Balents, and T. Senthil, Phys. Rev. B 69, 224416 (2004).
33. R. Moessner, O. Tchernyshyov, and S.L. Sondhi, J. Stat. Phys. 116, 755 (2004).
34. S. Chakravarty, Phys. Rev. B 66, 224505 (2002).
35. See Ref. 29 and Ph. Sindzingre (unpublished).
36. S. Isakov and R. Moessner (unpublished).