Anyonic entanglement renormalization

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 12, 2010, Pages

  König, Robert ^a   Bilgin, Ersen ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957729549     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.125118     Document Type: Article

References (73)

1. A. Y. Kitaev, Ann. Phys. 303, 2 (2003). 10.1016/S0003-4916(02)00018-0 (Pubitemid 36177417)
2. J. Preskill, "Topological quantum computation," Lecture Notes (Chap. 9), 2004, www.theory.caltech.edu/people/preskill/ph229/
3. M. Freedman, A. Kitaev, M. Larsen, and Z. Wang, Bull. Am. Math. Soc. 40, 31 (2003). 10.1090/S0273-0979-02-00964-3 (Pubitemid 36052318)
4. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008). 10.1103/RevModPhys.80.1083
5. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 10.1016/0550- 3213(91)90407-O
6. N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). 10.1103/PhysRevB.59. 8084
7. E. H. Rezayi and N. Read, Phys. Rev. B 79, 075306 (2009). 10.1103/PhysRevB.79.075306
8. M. Dolev, M. Heiblum, V. Umansky, A. Stern, and D. Mahalu, Nature (London) 452, 829 (2008) 10.1038/nature06855
9. arXiv:0802.0930 (unpublished).
10. I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Science 320, 899 (2008) 10.1126/science.1157560 (Pubitemid 351929581)
11. R. L. Willett, L. N. Pfeiffer, and K. W. West, Proc. Natl. Acad. Sci. U.S.A. 106, 8853 (2009). 10.1073/pnas.0812599106
12. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). 10.1103/PhysRevLett.95.226801 (Pubitemid 41776999)
13. J. E. Moore and L. Balents, Phys. Rev. B 75, 121306 (2007). 10.1103/PhysRevB.75.121306
14. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007). 10.1103/PhysRevLett.98.106803 (Pubitemid 46393379)
15. R. Roy, Phys. Rev. B 79, 195322 (2009). 10.1103/PhysRevB.79.195322
16. A. Kitaev, Ann. Phys. 321, 2 (2006) 10.1016/j.aop.2005.10.005 (Pubitemid 43072824)
17. M. A. Levin and X.-G. Wen, Phys. Rev. B 71, 045110 (2005) 10.1103/PhysRevB.71.045110 (Pubitemid 40418061)
18. L. Duan, E. Demler, and M. Lukin, Phys. Rev. Lett. 91, 090402 (2003) 10.1103/PhysRevLett.91.090402
19. A. Micheli, G. Brennen, and P. Zoller, Nat. Phys. 2, 341 (2006) 10.1038/nphys287 (Pubitemid 43787232)
20. S. Trebst, P. Werner, M. Troyer, K. Shtengel, and C. Nayak, Phys. Rev. Lett. 98, 070602 (2007) 10.1103/PhysRevLett.98.070602
21. J. Vidal, S. Dusuel, and K. P. Schmidt, Phys. Rev. B 79, 033109 (2009). 10.1103/PhysRevB.79.033109
22. J. Vidal, R. Thomale, K. P. Schmidt, and S. Dusuel, Phys. Rev. B 80, 081104 (2009). 10.1103/PhysRevB.80.081104
23. I. Tupitsyn, A. Kitaev, N. Prokof'ev, and P. Stamp, arXiv:0804.3175 (unpublished).
24. S. Bravyi and M. Hastings, arXiv:1001.4363 (unpublished).
25. S. Bravyi, M. B. Hastings, and S. Michalakis, arXiv:1001.0344 (unpublished).
26. I. Klich, arXiv:0912.0945 (unpublished).
27. P. Bonderson, Phys. Rev. Lett. 103, 110403 (2009) 10.1103/PhysRevLett. 103.110403
28. A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, Phys. Rev. Lett. 98, 160409 (2007) 10.1103/PhysRevLett.98. 160409 (Pubitemid 46633688)
29. L. Fidkowski, G. Refael, N. E. Bonesteel, and J. E. Moore, Phys. Rev. B 78, 224204 (2008). 10.1103/PhysRevB.78.224204
30. L. Fidkowski, H.-H. Lin, P. Titum, and G. Refael, Phys. Rev. B 79, 155120 (2009). 10.1103/PhysRevB.79.155120
31. N. E. Bonesteel and K. Yang, Phys. Rev. Lett. 99, 140405 (2007). 10.1103/PhysRevLett.99.140405 (Pubitemid 47549464)
32. S. R. White, Phys. Rev. Lett. 69, 2863 (1992). 10.1103/PhysRevLett.69. 2863
33. R. König, Phys. Rev. A 81, 052309 (2010). 10.1103/PhysRevA.81.052309
34. G. Vidal, Phys. Rev. Lett. 99, 220405 (2007). 10.1103/PhysRevLett.99. 220405 (Pubitemid 350191565)
35. G. Vidal, Phys. Rev. Lett. 101, 110501 (2008). 10.1103/PhysRevLett.101. 110501
36. S. Rommer and S. Östlund, Phys. Rev. B 55, 2164 (1997). 10.1103/PhysRevB.55.2164
37. G. Vidal, Phys. Rev. Lett. 93, 040502 (2004). 10.1103/PhysRevLett.93. 040502
38. F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004). 10.1103/PhysRevLett.93.227205 (Pubitemid 40072806)
39. F. Verstraete, V. Murg, and J. I. Cirac, Adv. Phys. 57, 143 (2008). 10.1080/14789940801912366
40. F. Verstraete and J. I. Cirac, Phys. Rev. B 73, 094423 (2006). 10.1103/PhysRevB.73.094423 (Pubitemid 43429335)
41. S. Trebst, M. Troyer, Z. Wang, and A. W. W. Ludwig, Prog. Theor. Phys. Suppl. 176, 384 (2008). 10.1143/PTPS.176.384
42. G. Evenbly and G. Vidal, New J. Phys. 12, 025007 (2010). 10.1088/1367-2630/12/2/025007
43. P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009). 10.1103/PhysRevB.80.165129
44. F. Verstraete and J. I. Cirac, Phys. Rev. A 70, 060302 (2004). 10.1103/PhysRevA.70.060302 (Pubitemid 40213784)
45. Z.-C. Gu, M. Levin, and X.-G. Wen, Phys. Rev. B 78, 205116 (2008). 10.1103/PhysRevB.78.205116
46. I. Pižorn and F. Verstraete, Phys. Rev. B 81, 245110 (2010). 10.1103/PhysRevB.81.245110
47. C. V. Kraus, N. Schuch, F. Verstraete, and J. I. Cirac, Phys. Rev. A 81, 052338 (2010). 10.1103/PhysRevA.81.052338
48. C. Pineda, T. Barthel, and J. Eisert, Phys. Rev. A 81, 050303 (2010). 10.1103/PhysRevA.81.050303
49. T. Barthel, C. Pineda, and J. Eisert, Phys. Rev. A 80, 042333 (2009). 10.1103/PhysRevA.80.042333
50. P. Corboz, R. Orús, B. Bauer, and G. Vidal, Phys. Rev. B 81, 165104 (2010). 10.1103/PhysRevB.81.165104
51. N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 98, 140506 (2007). 10.1103/PhysRevLett.98.140506 (Pubitemid 46557467)
52. G. Evenbly and G. Vidal, Phys. Rev. B 79, 144108 (2009) 10.1103/PhysRevB.79.144108
53. P. Silvi, V. Giovannetti, S. Montangero, M. Rizzi, J. I. Cirac, and R. Fazio, arXiv:0912.0466 (unpublished).
54. V. Giovannetti, S. Montangero, and R. Fazio, Phys. Rev. Lett. 101, 180503 (2008). 10.1103/PhysRevLett.101.180503
55. R. N. C. Pfeifer, G. Evenbly, and G. Vidal, Phys. Rev. A 79, 040301 (2009) 10.1103/PhysRevA.79.040301
56. K. Walker, "On Witten's three-manifold invariants," 1991, available at http://canyon23.net/math/
57. R. König, G. Kuperberg, and B. W. Reichardt, arXiv:1002.2816 (unpublished).
58. P. Bonderson, M. Freedman, and C. Nayak, Ann. Phys. 324, 787 (2009) 10.1016/j.aop.2008.09.009
59. C. Gils, E. Ardonne, S. Trebst, A. W. W. Ludwig, M. Troyer, and Z. Wang, Phys. Rev. Lett. 103, 070401 (2009). 10.1103/PhysRevLett.103.070401
60. V. Lahtinen, G. Kells, A. Carollo, T. Stitt, J. Vala, and J. K. Pachos, Ann. Phys. 323, 2286 (2008). 10.1016/j.aop.2007.12.009
61. M. Baraban, G. Zikos, N. Bonesteel, and S. H. Simon, Phys. Rev. Lett. 103, 076801 (2009). 10.1103/PhysRevLett.103.076801
62. M. Cheng, R. M. Lutchyn, V. Galitski, and S. Das Sarma, Phys. Rev. Lett. 103, 107001 (2009). 10.1103/PhysRevLett.103.107001
63. S. Montangero, M. Rizzi, V. Giovannetti, and R. Fazio, Phys. Rev. B 80, 113103 (2009) 10.1103/PhysRevB.80.113103
64. M. Aguado and G. Vidal, Phys. Rev. Lett. 100, 070404 (2008). 10.1103/PhysRevLett.100.070404 (Pubitemid 351393533)
65. C. K. Majumdar and D. K. Gosh, J. Math. Phys. 10, 1388 (1969). 10.1063/1.1664978
66. S. Trebst, E. Ardonne, A. Feiguin, D. A. Huse, A. W. W. Ludwig, and M. Troyer, Phys. Rev. Lett. 101, 050401 (2008) 10.1103/PhysRevLett.101.050401
67. G. E. Andrews, R. J. Baxter, and P. J. Forrester, J. Stat. Phys. 35, 193 (1984). 10.1007/BF01014383
68. A. W. W. Ludwig, D. Poilblanc, S. Trebst, and M. Troyer, arXiv:1003.3453 (unpublished).
69. R. König, B. W. Reichardt, and G. Vidal, Phys. Rev. B 79, 195123 (2009). 10.1103/PhysRevB.79.195123
70. Y.-Y. Shi, L.-M. Duan, and G. Vidal, Phys. Rev. A 74, 022320 (2006). 10.1103/PhysRevA.74.022320 (Pubitemid 44274283)
71. L. Tagliacozzo, G. Evenbly, and G. Vidal, Phys. Rev. B 80, 235127 (2009). 10.1103/PhysRevB.80.235127
72. V. Murg, Ö. Legeza, R. Noack, and F. Verstraete, arXiv:1006.3095 (unpublished).
73. R. Pfeifer, P. Corboz, O. Buerschaper, M. Aguado, M. Troyer, and G. Vidal, arXiv:1006.3532v1 (unpublished).