Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and px + ipy paired superfluids

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 4, 2009, Pages

  Read, N ^a  

^a Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59249089187     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.045308     Document Type: Article

References (103)

1. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991); 10.1016/0550- 3213(91)90407-O
2. N. Read and G. Moore, Prog. Theor. Phys. Suppl. 107, 157 (1992), and in Ref.. 10.1143/PTPS.107.157
3. A. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003). 10.1016/S0003-4916(02)00018-0
4. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 106, 162 (1957); 10.1103/PhysRev.106.162
5. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957). 10.1103/PhysRev.108.1175
6. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000). 10.1103/PhysRevB.61. 10267
7. M. H. Freedman, A. Kitaev, M. J. Larsen, and Z. Wang, arXiv:quant-ph/0101025 (unpublished).
8. J. E. Avron, R. Seiler, and P. G. Zograf, Phys. Rev. Lett. 75, 697 (1995). 10.1103/PhysRevLett.75.697
9. I. V. Tokatly and G. Vignale, Phys. Rev. B 76, 161305 (R) (2007). 10.1103/PhysRevB.76.161305
10. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). 10.1103/PhysRevLett.50. 1395
11. D. Arovas, J. R. Schrieffer, and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984). 10.1103/PhysRevLett.53.722
12. M. Stone, in The Quantum Hall Effect, edited by, M. Stone, (World Scientific, Singapore, 1992), Chap..
13. A. Seidel and D. H. Lee, Phys. Rev. B 76, 155101 (2007). 10.1103/PhysRevB.76.155101
14. A. Seidel, Phys. Rev. Lett. 101, 196802 (2008). 10.1103/PhysRevLett.101. 196802
15. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984). 10.1098/rspa.1984.0023
16. B. Simon, Phys. Rev. Lett. 51, 2167 (1983). 10.1103/PhysRevLett.51.2167
17. F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984). 10.1103/PhysRevLett.52.2111
18. B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984). 10.1103/PhysRevLett.52. 1583
19. P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory (Springer, New York, 1997).
20. G. Moore and N. Seiberg, Commun. Math. Phys. 123, 177 (1989). 10.1007/BF01238857
21. A. Belavin, A. Polyakov, and A. Zamolodchikov, Nucl. Phys. B 241, 333 (1984). 10.1016/0550-3213(84)90052-X
22. N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). 10.1103/PhysRevB.59. 8084
23. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971) pp. 495-499.
24. F. D. M. Haldane and Y.-S. Wu, Phys. Rev. Lett. 55, 2887 (1985). 10.1103/PhysRevLett.55.2887
25. S. M. Girvin and A. H. MacDonald, Phys. Rev. Lett. 58, 1252 (1987); 10.1103/PhysRevLett.58.1252
26. S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989); 10.1103/PhysRevLett.62.82
27. N. Read, Phys. Rev. Lett. 62, 86 (1989); 10.1103/PhysRevLett.62.86
28. J. K. Jain, Phys. Rev. Lett. 63, 199 (1989); 10.1103/PhysRevLett.63.199
29. J. K. Jain, Phys. Rev. B 40, 8079 (1989); 10.1103/PhysRevB.40.8079
30. J. K. Jain, Phys. Rev. B 41, 7653 (1990); 10.1103/PhysRevB.41.7653
31. A. Lopez and E. Fradkin, Phys. Rev. B 44, 5246 (1991); 10.1103/PhysRevB.44.5246
32. B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993); 10.1103/PhysRevB.47.7312
33. N. Read, Semicond. Sci. Technol. 9, 1859 (1994). 10.1088/0268-1242/9/11S/ 002
34. D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001). 10.1103/PhysRevLett.86.268
35. C. Nayak and F. Wilczek, Nucl. Phys. B 479, 529 (1996). 10.1016/0550-3213(96)00430-0
36. N. Read and E. Rezayi, Phys. Rev. B 54, 16864 (1996). 10.1103/PhysRevB.54.16864
37. V. F. R. Jones, in Geometric Methods in Operator Algebras: Proceedings of US-Japan Seminar, Kyoto, 1983, edited by, H. Araki, and E., G. Effros, (Wiley, New York, 1986).
38. N. Read, J. Math. Phys. 44, 558 (2003). 10.1063/1.1530369
39. A. Stern, F. von Oppen, and E. Mariani, Phys. Rev. B 70, 205338 (2004). 10.1103/PhysRevB.70.205338
40. M. Stone and S. B. Chung, Phys. Rev. B 73, 014505 (2006). 10.1103/PhysRevB.73.014505
41. V. Gurarie and C. Nayak, Nucl. Phys. B 506, 685 (1997). 10.1016/S0550-3213(97)00612-3
42. E. Fradkin, C. Nayak, A. Tsvelik, and F. Wilczek, Nucl. Phys. B 516, 704 (1998). 10.1016/S0550-3213(98)00111-4
43. E. Fradkin, C. Nayak, and K. Schoutens, Nucl. Phys. B 546, 711 (1999). 10.1016/S0550-3213(99)00039-5
44. Y. Tserkovnyak and S. H. Simon, Phys. Rev. Lett. 90, 016802 (2003). 10.1103/PhysRevLett.90.016802
45. B. Blok and X.-G. Wen, Nucl. Phys. B 374, 615 (1992). 10.1016/0550-3213(92)90402-W
46. S. B. Chung and M. Stone, J. Phys. A 40, 4923 (2007). 10.1088/1751-8113/40/19/001
47. E. Ardonne and K. Schoutens, Ann. Phys. 322, 201 (2007). 10.1016/j.aop.2006.07.015
48. J. E. Avron, J. Stat. Phys. 92, 543 (1998). 10.1023/A:1023084404080
49. E. M. Lifshitz and L. P. Pitaevskii, Landau and Lifshitz Course in Theoretical Physics, Physical Kinetics Vol. 10 (Pergamon, Oxford, 1981), p. 254.
50. P. Lévay, J. Math. Phys. 36, 2792 (1995). 10.1063/1.531066
51. J. R. Schrieffer, Theory of Superconductivity (Addison-Wesley, Reading, MA, 1964).
52. D. Vollhardt and P. Wölfle, The Superfluid Phases of Helium 3 (Taylor & Francis, London, 1990).
53. F. D. M. Haldane, Phys. Rev. Lett. 55, 2095 (1985). 10.1103/PhysRevLett. 55.2095
54. D. Mumford, Tata Lectures on Theta (Birkhäuser Boston, New York, 2007), Vol. 1, Chap..
55. A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185, 832 (1969). 10.1103/PhysRev.185.832
56. C. Itzykson and J.-M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989), Chap..
57. M. Milovanović and N. Read, Phys. Rev. B 53, 13559 (1996). 10.1103/PhysRevB.53.13559
58. H. Iwaniec, Topics in Classical Automorphic Forms, Graduate Studies in Mathematics Vol. 17 (American Mathematical Society, Providence, RI, 1997).
59. J. Cardy and I. Peschel, Nucl. Phys. B 300, 377 (1988). 10.1016/0550-3213(88)90604-9
60. A. M. Polyakov, Phys. Lett. 103B, 207 (1981).
61. O. Alvarez, Nucl. Phys. B 216, 125 (1983). 10.1016/0550-3213(83)90490-X
62. D. Mumford, The Red Book of Vareties and Schemes, 2nd ed. (Springer-Verlag, Berlin, 1999), Appendix: Curves and Their Jacobians.
63. B. Bakalov and A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series Vol. 21 (American Mathematical Society, Providence, RI, 2001).
64. V. G. Turaev, Quantum Invariants of Knots and Manifolds (Walter de Gruyter, Berlin, 1994).
65. E. Rowell, R. Stong, and Z. Wang, arXiv:0712.1377 (unpublished).
66. A. Kitaev, Ann. Phys. (N.Y.) 321, 2 (2006). 10.1016/j.aop.2005.10.005
67. N. Read and B. Chakraborty, Phys. Rev. B 40, 7133 (1989). 10.1103/PhysRevB.40.7133
68. F. D. M. Haldane and E. H. Rezayi, Phys. Rev. B 31, 2529 (1985). 10.1103/PhysRevB.31.2529
69. G. Cristofano, G. Maiella, R. Musto, and F. Nicodemi, Mod. Phys. Lett. A 6, 1779 (1991). 10.1142/S0217732391001925
70. B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993). 10.1103/PhysRevB.47.7312
71. J.-B. Zuber and C. Itzykson, Phys. Rev. D 15, 2875 (1977). 10.1103/PhysRevD.15.2875
72. N. Read, Phys. Rev. Lett. 62, 86 (1989). 10.1103/PhysRevLett.62.86
73. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973); 10.1088/0022-3719/6/7/010
74. J. M. Kosterlitz, J. Phys. C 7, 1046 (1974). 10.1088/0022-3719/7/6/005
75. S. M. Girvin, A. H. MacDonald, M. P. A. Fisher, S.-J. Rey, and J. P. Sethna, Phys. Rev. Lett. 65, 1671 (1990). 10.1103/PhysRevLett.65.1671
76. A. B. Zamolodchikov, JETP Lett. 43, 730 (1986).
77. Z. Wang (private communication).
78. R. de Gail, N. Regnault, and M. O. Goerbig, Phys. Rev. B 77, 165310 (2008). 10.1103/PhysRevB.77.165310
79. V. A. Fateev and A. B. Zamolodchikov, Phys. Lett. B 271, 91 (1991). 10.1016/0370-2693(91)91283-2
80. J. W. Reijnders, F. J. M. van Lankvelt, K. Schoutens, and N. Read, Phys. Rev. Lett. 89, 120401 (2002); 10.1103/PhysRevLett.89.120401
81. J. W. Reijnders, F. J. M. van Lankvelt, K. Schoutens, and N. Read, Phys. Rev. A 69, 023612 (2004). 10.1103/PhysRevA.69.023612
82. E. Ardonne and K. Schoutens, Phys. Rev. Lett. 82, 5096 (1999); 10.1103/PhysRevLett.82.5096
83. E. Ardonne, N. Read, E. Rezayi, and K. Schoutens, Nucl. Phys. B 607, 549 (2001). 10.1016/S0550-3213(01)00224-3
84. N. Read, arXiv:0711.0543 (unpublished).
85. J. Polchinski, Nucl. Phys. B 303, 226 (1988). 10.1016/0550-3213(88)90179- 4
86. V. Riva and J. Cardy, Phys. Lett. B 622, 339 (2005).
87. S. H. Simon, E. H. Rezayi, N. R. Cooper, and I. Berdnikov, Phys. Rev. B 75, 075317 (2007). 10.1103/PhysRevB.75.075317
88. S. H. Simon (private communication).
89. S. H. Simon, E. H. Rezayi, and N. R. Cooper, Phys. Rev. B 75, 195306 (2007). 10.1103/PhysRevB.75.195306
90. B. A. Bernevig and F. D. M. Haldane, Phys. Rev. Lett. 100, 246802 (2008); 10.1103/PhysRevLett.100.246802
91. B. A. Bernevig and F. D. M. Haldane, Phys. Rev. B 77, 184502 (2008); 10.1103/PhysRevB.77.184502
92. B. A. Bernevig and F. D. M. Haldane, Phys. Rev. Lett. 101, 246806 (2008). 10.1103/PhysRevLett.101.246806
93. X.-G. Wen and Z. Wang, arXiv:0801.3291 (unpublished);
94. arXiv:0803.1016 (unpublished).
95. F. D. M. Haldane and E. H. Rezayi, Phys. Rev. Lett. 60, 956 (1988). 10.1103/PhysRevLett.60.956
96. D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B 271, 93 (1986).
97. D. Green, N. Read, and E. H. Rezayi (unpublished);
98. D. Green, Ph.D. thesis, Yale University, 2001.
99. X.-G. Wen and Y.-S. Wu, Nucl. Phys. B 419, 455 (1994); 10.1016/0550-3213(94)90340-9
100. X.-G. Wen, Y.-S. Wu, and Y. Hatsugai, Nucl. Phys. B 422, 476 (1994). 10.1016/0550-3213(94)90442-1
101. L. Dixon, D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B 282, 13 (1987). 10.1016/0550-3213(87)90676-6
102. M. R. Gaberdiel and H. G. Kausch, Nucl. Phys. B 477, 293 (1996). 10.1016/0550-3213(96)00364-1
103. N. Read, arXiv:0807.3107 (unpublished).