Line of critical points in 2+1 dimensions: Quantum critical loop gases and non-abelian gauge theory

Physical Review Letters

Volumn 94, Issue 14, 2005, Pages

  Freedman, Michael ^a   Nayak, Chetan ^a,b   Shtengel, Kirill ^a,c  

^a MICROSOFT RESEARCH   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c California Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHERN-SIMONS THEORY; NON-ABELIAN GAGE THEORY; QUANTUM NUMBER; UNIVERSALITY CLASS;

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; GROUND STATE; HAMILTONIANS; PERTURBATION TECHNIQUES; STATISTICAL MECHANICS; THERMODYNAMICS; TOPOLOGY;

QUANTUM THEORY;

EID: 18144391591     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.94.147205     Document Type: Article

References (25)

1. Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures, edited by S. Das Sarma and A. Pinczek (Wiley, New York, 1997), and references therein.
2. X. G. Wen, Int. J. Mod. Phys. B 4, 239 (1990).
3. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
4. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
5. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
6. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
7. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
8. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
9. P. W. Anderson, Science 235, 1196 (1987); S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987); N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B 61, 6307 (2000); T. Senthil and M. P. A. Fisher, Phys. Rev. B 62, 7850 (2000); R. B. Laughlin, Phys. Rev. Lett. 60, 2677 (1988); Y. Chen, F. Wilczek, E. Witten, and B. Halperin, Int. J. Mod. Phys. B 3, 1001 (1989).
10. A. Y. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003).
11. M. H. Freedman, M. J. Larsen, and Z. Wang, Commun. Math. Phys. 227, 605 (2002).
12. M. Freedman et al., Ann. Phys. (N.Y.) 310, 428 (2004).
13. M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. Lett. 94, 066401 (2005).
14. B. Nienhuis, in Phase Transitions and Critical Phenomena, Vol. 11, edited by C. Domb and J. Liebowitz (Academic Press, Singapore, 1987).
15. H. Saleur and B. Duplantier, Phys. Rev. Lett. 58, 2325 (1987).
16. M. H. Freedman, Commun. Math. Phys. 234, 129 (2003).
17. V. G. Turaev and O. Y. Viro, Topology 31, 865 (1992).
18. M. Freedman, C. Nayak, and K. Shtengel (unpublished).
19. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
20. The U(1) version of this theory was proposed in C. L. Henley, J. Stat. Phys. 89, 483 (1997); R. Moessner et al., Phys. Rev. B 65, 024504 (2002); E. Fradkin et al., Phys. Rev. B 69, 224415 (2004); and A. Vishwanath et al., Phys. Rev. B 69, 224416 (2004) for the critical point of the square lattice quantum dimer model introduced in [13].
21. The U(1) version of this theory was proposed in C. L. Henley, J. Stat. Phys. 89, 483 (1997); R. Moessner et al., Phys. Rev. B 65, 024504 (2002); E. Fradkin et al., Phys. Rev. B 69, 224415 (2004); and A. Vishwanath et al., Phys. Rev. B 69, 224416 (2004) for the critical point of the square lattice quantum dimer model introduced in [13].
22. The U(1) version of this theory was proposed in C. L. Henley, J. Stat. Phys. 89, 483 (1997); R. Moessner et al., Phys. Rev. B 65, 024504 (2002); E. Fradkin et al., Phys. Rev. B 69, 224415 (2004); and A. Vishwanath et al., Phys. Rev. B 69, 224416 (2004) for the critical point of the square lattice quantum dimer model introduced in [13].
23. The U(1) version of this theory was proposed in C. L. Henley, J. Stat. Phys. 89, 483 (1997); R. Moessner et al., Phys. Rev. B 65, 024504 (2002); E. Fradkin et al., Phys. Rev. B 69, 224415 (2004); and A. Vishwanath et al., Phys. Rev. B 69, 224416 (2004) for the critical point of the square lattice quantum dimer model introduced in [13].
24. M. Peskin and B. Schroeder, An Introduction to Quantum Field Theory (Perseus, New York, 1995).
25. M. H. Freedman, Found. Comput. Math. 1, 183 (2001), and references therein.