Three-dimensional topological lattice models with surface anyons

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 4, 2013, Pages

  Von Keyserlingk, C W ^a   Burnell, F J ^a   Simon, S H ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84872892560     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.045107     Document Type: Article

References (53)

1. D. Arovas, J. R. Schrieffer, and F. Wilczek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.53.722 53, 722 (1984).
2. C. Nayak, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.1083 80, 1083 (2008).
3. M. Freedman, M. B. Hastings, C. Nayak, X.-L. Qi, K. Walker, and Z. Wang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.115132 83, 115132 (2011).
4. J. C. Y. Teo and C. L. Kane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.046401 104, 046401 (2010).
5. M. Levin, F. J. Burnell, M. Koch-Janusz, and A. Stern, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.235145 84, 235145 (2011).
6. J. Maciejko, X. L. Qi, A. Karch, and S. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.246809 105, 246809 (2010).
7. B. Swingle, M. Barkeshli, J. McGreevy, and T. Senthil, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.195139 83, 195139 (2011).
8. Kevin Walker and Zhenghan Wang, Front. Phys. 2095-0462 10.1007/s11467-011-0194-z 7, 150 (2012).
9. M. A. Levin and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.045110 71, 045110 (2005). (Pubitemid 40418061)
10. X.-G. Wen (private communication).
11. D. B. Kaplan, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(92)91112-M 288, 342 (1992).
12. A. Kitaev, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0 303, 2 (2003). (Pubitemid 36177417)
13. A. Hamma, P. Zanardi, and X.-G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.035307 72, 035307 (2005). (Pubitemid 41506716)
14. M. Freedman, C. Nayak, K. Shtengel, K. Walker, and Z. Wang, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/j.aop.2004.01.006 310, 428 (2004). (Pubitemid 38457639)
15. A. Kitaev, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/j.aop.2005.10.005 321, 2 (2006). (Pubitemid 43072824)
16. Trivalent vertices are used because vertices with higher valence require an additional quantum label, which complicates the Hamiltonian.
17. C. Castelnovo and C. Chamon, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.155120 78, 155120 (2008).
18. H. Bombin and M. A. Martin-Delgado, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.075103 75, 075103 (2007).
19. R between the ground-state amplitudes of the configurations on the left (L) and right (R) of Eq..
20. Alexei Kitaev and Liang Kong, Commun. Math. Phys. 0010-3616 10.1007/s00220-012-1500-5 313, 351 (2012).
21. S. B. Bravyi, A. Yu. Kitaev, arXiv: quant-ph/9811052.
22. F. A. Bais and J. K. Slingerland, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.045316 79, 045316 (2009).
23. T. Hansson, V. Oganesyan, and S. Sondhi, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/j.aop.2004.05.006 313, 497 (2004). (Pubitemid 39603439)
24. G. T. Horowitz, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01218410 125, 417 (1989).
25. R. J. Szabo, Ann. Phys. (NY) APNYA6 0003-4916 10.1006/aphy.1999.5986 280, 163 (2000).
26. We thank Xiao-Liang Qi for bringing this to our attention.
27. T. Banks, R. Myerson, and J. B. Kogut, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(77)90129-8 129, 493 (1977).
28. A. M. Polyakov, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(75) 90162-8 59, 82 (1975).
29. J. L. Cardy and E. Rabinovici, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(82)90463-1 205, 1 (1982).
30. C. W. von Keyserlingk, F. J. Burnell, and S. H. Simon (unpublished).
31. Z. Wang, Topological Quantum Computation, CBMS Regional Conference Series in Mathematics, 112 (American Mathematical Society, Providence, RI, 2010).
32. P. Bonderson, Ph.D. thesis, California Institute of Technology, Pasadena, 2007.
33. In fuller generality, the vertices can also carry a quantum label when the underlying category has "fusion multiplicities" (Ref.). We do not consider this here. In addition, the strings in the categories can be oriented. This makes little difference to the qualitative behavior of the models.
34. Adam S. Sikora, in Knots in Hellas '98, Proceedings of the International Conference on Knot Theory, edited by, C. McA. Gordon, (World Scientific, Singapore, 2000).
35. Michael E. Peskin and Daniel V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995).
36. A. S. Cattaneo and C. A. Rossi, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-005-1339-0 256, 513 (2005). (Pubitemid 40630673)
37. X.-G. Wen, Quantum Field Theory of Many-Body Systems ÑFrom the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, Oxford, UK, 2004).
38. J. Maciejko, X.-L. Qi, A. Karch, and S.-C. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.235128 86, 235128 (2012).
39. There is an extra complication that this category comes with oriented strings, but we can ignore this subtlety if we choose a convention for orienting the edges of our lattice.
40. E. Witten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01217730 121, 351 (1989).
41. R. Dijkgraaf and E. Witten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02096988 129, 393 (1990).
42. X. G. Wen and A. Zee, Nucl. Phys. B NPBSE7 0920-5632 10.1016/0920- 5632(90)90014-L 15, 135 (1990);
43. X. G. Wen and A. Zee, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44. 274 44, 274 (1991).
44. G. Moore and N. Read, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550- 3213(91)90407-O 360, 362 (1991).
45. For a similar model with a gapless surface Majorana mode, see S. Ryu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.075124 79, 075124 (2009).
46. M. de Wild Propitius and F. A. Bais, arXiv: hep-th/9511201;
47. M. de Wild Propitius, arXiv: hep-th/9511195;
48. E. Fradkin and S. H. Shenker, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.19.3682 19, 3682 (1979).
49. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.195125 78, 195125 (2008).
50. Ashvin Vishwanath and T. Senthil, arXiv: 1209.3058.
51. F. J. Burnell, S. H. Simon, and J. K. Slingerland, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.125434 84, 125434 (2011).
52. F. J. Burnell and J. Cardy (unpublished).
53. Michael Levin and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.110405 96, 110405 (2006).