Classifying fractionalization: Symmetry classification of gapped Z 2 spin liquids in two dimensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 10, 2013, Pages

  Essin, Andrew M ^a   Hermele, Michael ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84875291708     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.104406     Document Type: Article

References (57)

1. X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.7387 40, 7387 (1989).
2. X.-G. Wen, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S0217979290000139 4, 239 (1990).
3. X.-G. Wen, arXiv: 1210.1281.
4. R. B. Laughlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50. 1395 50, 1395 (1983).
5. C. L. Kane and M. P. A. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.724 72, 724 (1994).
6. R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, and D. Mahalu, Nature NATUAS 0028-0836 10.1038/38241 389, 162 (1997). (Pubitemid 27400593)
7. L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.2526 79, 2526 (1997).
8. A. Stern, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2007.10.008 323, 204 (2008).
9. F. J. Wegner, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1665530 12, 2259 (1971).
10. N. Read and B. Chakraborty, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.7133 40, 7133 (1989).
11. N. Read and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.1773 66, 1773 (1991).
12. X. G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44.2664 44, 2664 (1991).
13. L. Balents, M. P. A. Fisher, and C. Nayak, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.60.1654 60, 1654 (1999).
14. T. Senthil and M. P. A. Fisher, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.62.7850 62, 7850 (2000). (Pubitemid 32336153)
15. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1881 86, 1881 (2001). (Pubitemid 32252800)
16. R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.024504 65, 024504 (2001).
17. L. Balents, M. P. A. Fisher, and S. M. Girvin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.224412 65, 224412 (2002).
18. A. Yu. Kitaev, Ann. Phys. APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0 303, 2 (2003). (Pubitemid 36177417)
19. X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.165113 65, 165113 (2002).
20. X.-G. Wen, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.68.065003 68, 065003 (2003). (Pubitemid 44652415)
21. F. Wang and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.174423 74, 174423 (2006). (Pubitemid 44791132)
22. S.-P. Kou, M. Levin, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.155134 78, 155134 (2008).
23. S.-P. Kou and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.224406 80, 224406 (2009).
24. H. Yao, L. Fu, and X.-L. Qi, arXiv: 1012.4470.
25. Y. Huh, M. Punk, and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.094419 84, 094419 (2011).
26. G. Chen, A. Essin, and M. Hermele, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.094418 85, 094418 (2012).
27. M. Levin and A. Stern, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86. 115131 86, 115131 (2012).
28. G. Y. Cho, Y.-M. Lu, and J. E. Moore, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.125101 86, 125101 (2012).
29. S. Yan, D. A. Huse, and S. R. White, Science SCIEAS 0036-8075 10.1126/science.1201080 332, 1173 (2011).
30. L. Wang, Z.-C. Gu, F. Verstraete, and X.-G. Wen, arXiv: 1112.3331.
31. H.-C. Jiang, H. Yao, and L. Balents, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.024424 86, 024424 (2012).
32. S. Depenbrock, I. P. McCulloch, and U. Schollwöck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.067201 109, 067201 (2012).
33. H.-C. Jiang, Z. Wang, and L. Balents, Nat. Phys. 1745-2473 10.1038/nphys2465 8, 902 (2012).
34. F. Mezzacapo, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.045115 86, 045115 (2012).
35. A. Kitaev, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2005.10.005 321, 2 (2006). (Pubitemid 43072824)
36. A. Kitaev (private communication).
37. Y. Ran and X.-G. Wen (unpublished).
38. A. Paramekanti and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.245118 70, 245118 (2004). (Pubitemid 40362435)
39. Y.-Z. You and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.161107 86, 161107 (2012).
40. M. Hamermesh, Group Theory (Addison-Wesley, 1962).
41. M. V. Murthy, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1931219 7, 853 (1966).
42. S. Mac Lane, Homology (Springer-Verlag, 1975).
43. P. M. van den Broek, J. Phys. A 1361-6447 10.1088/0305-4470/9/6/007 9, 855 (1976).
44. X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.035107 83, 035107 (2011).
45. X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, arXiv: 1106.4772.
46. N. D. Mermin, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.64.3 64, 3 (1992).
47. C. J. Bradley, J. Phys. A JPMNAX 0301-0015 10.1088/0305-4470/6/12/007 6, 1843 (1973).
48. X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press, 2004).
49. A. M. Essin (unpublished).
50. Y.-M. Lu and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.125119 86, 125119 (2012).
51. A. M. Turner, F. Pollmann, and E. Berg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.075102 83, 075102 (2011).
52. L. Fidkowski and A. Kitaev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.075103 83, 075103 (2011).
53. N. Schuch, D. Pérez-García, and I. Cirac, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.165139 84, 165139 (2011).
54. A. Vishwanath and T. Senthil, Phys. Rev. X 10.1103/PhysRevX.3.011016 3, 011016 (2013).
55. M. B. Hastings, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.104431 69, 104431 (2004).
56. A. Mesaros and Y. Ran, arXiv: 1212.0835.
57. L.-Y. Hung and X.-G. Wen, arXiv: 1212.1827.