Topological Phases with Parafermions: Theory and Blueprints

Annual Review of Condensed Matter Physics

Volumn 7, Issue , 2016, Pages 119-139

  Alicea, Jason ^a,b,c   Fendley, Paul ^d  

^a California Institute of Technology   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d ALL SOULS COLLEGE   (United Kingdom)

Author keywords

Non Abelian anyons; Quantum Hall effect; Superconductivity; Topological quantum computation

Indexed keywords

BLUEPRINTS; CHAINS; COMPUTATION THEORY; COMPUTER HARDWARE; QUANTUM COMPUTERS; QUANTUM THEORY; SUPERCONDUCTIVITY; TOPOLOGY;

DECOHERENCE; NON-ABELIAN ANYONS; QUANTUM HALL; QUANTUM HALL BILAYERS; QUANTUM SPIN CHAINS; TOPOLOGICAL INSULATORS; TOPOLOGICAL PHASE; TOPOLOGICAL PHASIS;

QUANTUM HALL EFFECT;

EID: 84962567736     PISSN: 19475454     EISSN: 19475462     Source Type: Journal    
DOI: 10.1146/annurev-conmatphys-031115-011336     Document Type: Review

References (108)

1. Kitaev AY. 2003. Ann. Phys. 303:2
2. Nayak C, Simon SH, Stern A, Freedman M, Das Sarma S. 2008. Rev. Mod. Phys. 80:1083
3. Schultz TD, Mattis DC, Lieb EH. 1964. Rev. Mod. Phys. 36:856
4. McCoy BM, Wu TT. 2014. The Two-Dimensional Ising Model. New York: Dover. 2nd ed
5. Kitaev AY. 2001. Sov. Phys.-Uspeki 44:131
6. Pfeuty P. 1970. Ann. Phys. 57:179
7. Read N, Green D. 2000. Phys. Rev. B 61:10267
8. Ivanov DA. 2001. Phys. Rev. Lett. 86:268
9. Alicea J, Oreg Y, Refael G, von Oppen F, Fisher MPA. 2011. Nat. Phys. 7:412
10. Beenakker CWJ. 2013. Annu. Rev. Condens. Matter Phys. 4:113
11. Alicea J. 2012. Rep. Prog. Phys. 75:076501
12. Leijnse M, Flensberg K. 2012. Semicond. Sci. Technol. 27:124003
13. Stanescu TD, Tewari S. 2013. J. Phys.: Condens. Matter 25:233201
14. Elliott SR, Franz M. 2015. Rev. Mod. Phys. 87:137
15. Das Sarma S, Freedman M, Nayak C. 2015. NPJ Quant. Inf. Accepted. arXiv:1501.02813
16. Nussinov Z, van den Brink J. 2015. Rev. Mod. Phys. 87:1
17. Fendley P. 2012. J. Stat. Mech. 2012:11020
18. Fradkin E, Kadanoff LP. 1980. Nucl. Phys. B 170:1
19. Ostlund S. 1981. Phys. Rev. B 24:398
20. Huse D. 1981. Phys. Rev. B 24:5180
21. Howes S, Kadanoff L, Den Nijs M. 1983. Nucl. Phys. B 215:169
22. Au-Yang H, Perk JHH. 1997. Int. J. Mod. Phys. B 11:11
23. Motruk J, Berg E, Turner AM, Pollmann F. 2013. Phys. Rev. B 88:085115
24. Bondesan R, Quella T. 2013. J. Stat. Mech. 2013:P10024
25. Mong RSK, Clarke DJ, Alicea J, Lindner NH, Fendley P. 2014. J. Phys. A: Math. Theor. 47:452001
26. Baxter RJ. 2008. Exactly Solved Models in Statistical Mechanics. New York: Dover
27. Li W, Yang S, Tu H-H, Cheng M. 2015. Phys. Rev. B 91:115133
28. Alexandradinata A, Regnault N, Fang C, Gilbert M, Bernevig B. 2015. Parafermionic phases with symmetry-breaking and topological order. arXiv:1506.03455
29. Au-Yang H, McCoy BM, Perk JHH, Tang S, Yan M-L. 1987. Phys. Lett. A 123:219
30. Albertini G, McCoy BM, Perk JHH. 1989. Phys. Lett. A 139:204
31. McCoy BM, shyr Roan S. 1990. Phys. Lett. A 150:347
32. Zhuang Y, Changlani HJ, Tubman NM, Hughes TL. 2015. Phase diagram of the Z3 parafermionic chain with chiral interactions. arXiv:1502.05049
33. Jin B-Q, Au-Yang H, Perk JHH. 2002. Int. J. Mod. Phys. B 16:1979
34. Alcaraz FC, Köberle R. 1981. Phys. Rev. D 24:1562
35. Cobanera E, Ortiz G. 2014. Phys. Rev. A 89:012328
36. Baxter R. 1989. J. Stat. Phys. 57:1
37. Fendley P. 2014. J. Phys. A: Math. Theor. 47:075001
38. Huse DA, Nandkishore R, Oganesyan V, Pal A, Sondhi SL. 2013. Phys. Rev. B 88:014206
39. Jermyn AS, Mong RSK, Alicea J, Fendley P. 2014. Phys. Rev. B 90:165106
40. Bauer B, Nayak C. 2013. J. Stat. Mech.: Theory Exp. 2013:P09005
41. Bahri Y, Vosk R, Altman E, Vishwanath A. 2015. Nat. Comm. 6:7341
42. Zamolodchikov AB, Fateev V. 1985. J. Exp. Theor. Phys. 62:215, Zh. Eksp. Teor. Fiz. 89:380-99
43. Mong RSK, Clarke DJ, Alicea J, Lindner NH, Fendley P, et al. 2014. Phys. Rev. X 4:011036
44. Fidkowski L, Kitaev A. 2010. Phys. Rev. B 81:134509
45. Turner AM, Pollmann F, Berg E. 2011. Phys. Rev. B 83:075102
46. Chen X, Gu Z-C, Wen X-G. 2011. Phys. Rev. B 84:235128
47. Schuch N, Pérez-Garca D, Cirac I. 2011. Phys. Rev. B 84:165139
48. Barkeshli M, Qi X-L. 2012. Phys. Rev. X 2:031013
49. You Y-Z,Wen X-G. 2012. Phys. Rev. B 86:161107
50. Cheng M. 2012. Phys. Rev. B 86:195126
51. Vaezi A. 2013. Phys. Rev. B 87:035132
52. Klinovaja J, Yacoby A, Loss D. 2014. Phys. Rev. B 90:155447
53. Milsted A, Cobanera E, Burrello M, Ortiz G. 2014. Phys. Rev. B 90:195101
54. Maghrebi MF, Ganeshan S, Clarke DJ, Gorshkov AV, Sau JD. 2015. Parafermionic zero modes in ultracold bosonic systems. arXiv:1504.04012
55. Fu L, Kane CL. 2009. Phys. Rev. B 79:161408(R)
56. Lutchyn RM, Sau JD, Das Sarma S. 2010. Phys. Rev. Lett. 105:077001
57. Oreg Y, Refael G, von Oppen F. 2010. Phys. Rev. Lett. 105:177002
58. Lindner NH, Berg E, Refael G, Stern A. 2012. Phys. Rev. X 2:041002
59. Clarke DJ, Alicea J, Shtengel K. 2013. Nat. Commun. 4:1348
60. Clarke DJ, Alicea J, Shtengel K. 2014. Nat. Phys. 10:877
61. You Y-Z, Jian C-M, Wen X-G. 2013. Phys. Rev. B 87:045106
62. Sengupta K, Z utić I, Kwon H-J, Yakovenko VM, Das Sarma S. 2001. Phys. Rev. B 63:144531
63. Law KT, Lee PA, Ng TK. 2009. Phys. Rev. Lett. 103:237001
64. Fidkowski L, Alicea J, Lindner NH, Lutchyn RM, Fisher MPA. 2012. Phys. Rev. B 85:245121
65. Beenakker CWJ. 2015. Rev. Mod. Phys. 87:1037
66. BarkeshliM,OregY,QiX-L. 2014. Experimental proposal to detect topological ground state degeneracy. arXiv:1401.3750
67. Cheng M, Lutchyn RM. 2015. Fractional Josephson effect in number-conserving systems. arXiv:1502.04712
68. Bombin H. 2010. Phys. Rev. Lett. 105:030403
69. Barkeshli M,Wen X-G. 2010. Phys. Rev. B 81:045323
70. Barkeshli M, Jian C-M, Qi X-L. 2013. Phys. Rev. B 87:045130
71. Barkeshli M, Jian C-M, Qi X-L. 2013. Phys. Rev. B 88:241103
72. Barkeshli M, Jian C-M, Qi X-L. 2013. Phys. Rev. B 88:235103
73. Kapustin A. 2014. Phys. Rev. B 89:125307
74. Teo JCY, Roy A, Chen X. 2014. Phys. Rev. B 90:115118
75. Teo JCY, Roy A, Chen X. 2014. Phys. Rev. B 90:155111
76. Khan MN, Teo JCY, Hughes TL. 2014. Phys. Rev. B 90:235149
77. Wang J, Santos LH,Wen X-G. 2015. Phys. Rev. B 91:195134
78. Lan T,Wang JC, Wen X-G. 2015. Phys. Rev. Lett. 114:076402
79. Barkeshli M, Bonderson P, Cheng M, Wang Z. 2014. Symmetry, defects, and gauging of topological phases. arXiv:1410.4540
80. Teo JCY, Hughes TL, Fradkin E. 2015. Ann. Phys. 360:349
81. Hastings MB, Nayak C,Wang Z. 2013. Phys. Rev. B 87:165421
82. Barkeshli M, Qi X-L. 2014. Phys. Rev. X 4:041035
83. Zhang F, Kane CL. 2014. Phys. Rev. Lett. 113:036401
84. Orth CP, Tiwari RP, Meng T, Schmidt TL. 2015. Phys. Rev. B 91:081406
85. Xu C, Moore JE. 2006. Phys. Rev. B 73:045322
86. Oreg Y, Sela E, Stern A. 2014. Phys. Rev. B 89:115402
87. Klinovaja J, Loss D. 2014. Phys. Rev. Lett. 112:246403
88. Klinovaja J, Loss D. 2014. Phys. Rev. B 90:045118
89. Tsvelik AM. 2014. ZN parafermion zero modes without fractional quantum Hall effect. arXiv:1407.4002
90. Stoudenmire EM, Clarke DJ, Mong RSK, Alicea J. 2015. Phys. Rev. B 91:235112
91. Read N, Rezayi E. 1999. Phys. Rev. B 59:8084
92. Moore G, Read N. 1991. Nucl. Phys. B 360:362
93. Freedman MH, Larsen MJ,Wang Z. 2002. Commun. Math. Phys. 227:605
94. Freedman MH, Larsen MJ,Wang Z. 2002. Commun. Math. Phys. 228:177
95. Teo JCY, Kane CL. 2014. Phys. Rev. B 89:085101
96. Vaezi A. 2014. Phys. Rev. X 4:031009
97. Fateev VA. 1991. Int. J. Mod. Phys. A 6:2109
98. Vaezi A, Barkeshli M. 2014. Phys. Rev. Lett. 113:236804
99. Sagi E, Oreg Y. 2014. Phys. Rev. B 90:201102
100. Meng T, Neupert T, Greiter M, Thomale R. 2015. Coupled wire construction of chiral spin liquids. arXiv:1503.05051
101. Barkeshli M, Jiang H-C, Thomale R, Qi X-L. 2015. Phys. Rev. Lett. 114:026401
102. Burrello M, van Heck B, Cobanera E. 2013. Phys. Rev. B 87:195422
103. Wan Z, Kazakov A, Manfra MJ, Pfeiffer LN, West KW, Rokhinson LP. 2015. Nat. Comm. 6:7426
104. Hart S, Ren H,Wagner T, Leubner P, Muhlbauer M, et al. 2014. Nat. Phys. 10:638
105. Pribiag VS, Beukman AJA, Qu F, Cassidy MC, Charpentier C, et al. 2015. Nat. Nanotechnol. 10:593
106. Geraedts S, Zaletel MP, Papic Z, Mong RSK. 2015. Phys. Rev. B 91:205139
107. Peterson MR,Wu Y-L, Cheng M, Barkeshli M,Wang Z, Sarma SD. 2015. Phys. Rev. B 92:035103
108. Liu Z, Vaezi A, Lee K, Kim E-A. 2015. Non-Abelian phases in two-component v=2/3 fractional quantum Hall states: Emergence of Fibonacci anyons. arXiv:1502.05391