Coupled-wire constructions: a Luttinger liquid approach to topology

Abstract

Coupled-wire constructions use bosonization to analytically tackle the strong interactions underlying fractional topological states of matter. We give an introduction to this technique, discuss its strengths and weaknesses, and provide an overview of the main achievements of coupled-wire constructions.

References

  1. 1.

    K.v. Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

    ADS  Article  Google Scholar 

  2. 2.

    R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    ADS  Article  Google Scholar 

  3. 3.

    S.M. Girvin, The Quantum Hall Effect: Novel Excitations And Broken Symmetries, inAspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems, edited by A. Comtet, T. Jolicœur, S. Ouvry, F. David (Springer, Berlin, Heidelberg, 1999), pp. 53–175

  4. 4.

    X.G. Wen,Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons (Oxford University Press, Oxford, 2004)

  5. 5.

    E. Fradkin,Field Theories of Condensed Matter Physics, 2nd edn. (Cambridge University Press, 2013)

  6. 6.

    A. Altland, B.D. Simons,Condensed Matter Field Theory, 2nd edn. (Cambridge University Press, 2010)

  7. 7.

    D. Tong, https://arXiv:1606.06687 (2016)

  8. 8.

    V. Kalmeyer, R.B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987)

    ADS  Article  Google Scholar 

  9. 9.

    N. Read, D. Green, Phys. Rev. B 61, 10267 (2000)

    ADS  Article  Google Scholar 

  10. 10.

    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)

    ADS  Article  Google Scholar 

  11. 11.

    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)

    ADS  Article  Google Scholar 

  12. 12.

    B.A. Bernevig, S.C. Zhang, Phys. Rev. Lett. 96, 106802 (2006)

    ADS  Article  Google Scholar 

  13. 13.

    F.D.M.Haldane, Phys. Rev. Lett. 51, 605 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  14. 14.

    S.M. Girvin, A.H. MacDonald, P.M. Platzman, Phys. Rev. B 33, 2481 (1986)

    ADS  Article  Google Scholar 

  15. 15.

    S.C. Zhang, T.H. Hansson, S. Kivelson, Phys. Rev. Lett. 62, 82 (1989)

    ADS  Article  Google Scholar 

  16. 16.

    D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)

    ADS  Article  Google Scholar 

  17. 17.

    J.T. Chalker, P.D. Coddington, J. Phys. C: Solid State Phys. 21, 2665 (1988)

    ADS  Article  Google Scholar 

  18. 18.

    D.H. Lee, Phys. Rev. B 50, 10788 (1994)

    ADS  Article  Google Scholar 

  19. 19.

    P.M. Chaikin, M.Y. Choi, J.F. Kwak, J.S. Brooks, K.P. Martin, M.J. Naughton, E.M. Engler, R.L. Greene, Phys. Rev. Lett. 51, 2333 (1983)

    ADS  Article  Google Scholar 

  20. 20.

    M. Ribault, J. Cooper, D. Jérome, D. Mailly, A. Moradpour, K. Bechgaard, J. Physique Lett. 45, 935 (1984)

    Article  Google Scholar 

  21. 21.

    R.V. Chamberlin, M.J. Naughton, X. Yan, L.Y. Chiang, S.Y. Hsu, P.M. Chaikin, Phys. Rev. Lett. 60, 1189 (1988)

    ADS  Article  Google Scholar 

  22. 22.

    J.R. Cooper, W. Kang, P. Auban, G. Montambaux, D. Jérome, K. Bechgaard, Phys. Rev. Lett. 63, 1984 (1989)

    ADS  Article  Google Scholar 

  23. 23.

    S.T. Hannahs, J.S. Brooks, W. Kang, L.Y. Chiang, P.M. Chaikin, Phys. Rev. Lett. 63, 1988 (1989)

    ADS  Article  Google Scholar 

  24. 24.

    L. Balicas, G. Kriza, F.I.B. Williams, Phys. Rev. Lett. 75, 2000 (1995)

    ADS  Article  Google Scholar 

  25. 25.

    G. Montambaux, D. Zanchi, Synth. Met. 86, 2235 (1997)

    Article  Google Scholar 

  26. 26.

    C.L. Kane, R. Mukhopadhyay, T.C. Lubensky, Phys. Rev. Lett. 88, 036401 (2002)

    ADS  Article  Google Scholar 

  27. 27.

    D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

    ADS  Article  Google Scholar 

  28. 28.

    V.J. Goldman, B. Su, Science 267, 1010 (1995)

    ADS  Article  Google Scholar 

  29. 29.

    L. Saminadayar, D.C. Glattli, Y. Jin, B. Etienne, Phys. Rev. Lett. 79, 2526 (1997)

    ADS  Article  Google Scholar 

  30. 30.

    R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, D. Mahalu, Nature 389, 162 (1997)

    ADS  Article  Google Scholar 

  31. 31.

    T. Giamarchi,Quantum Physics in One Dimension (Oxford University Press, 2003)

  32. 32.

    J. von Delft, H. Schoeller, Ann. Phys. 7, 225 (1998)

    MathSciNet  Article  Google Scholar 

  33. 33.

    P. Szumniak, J. Klinovaja, D. Loss, Phys. Rev. B 93, 245308 (2016)

    ADS  Article  Google Scholar 

  34. 34.

    A. Luther, V.J. Emery, Phys. Rev. Lett. 33, 589 (1974)

    ADS  Article  Google Scholar 

  35. 35.

    J.C.Y. Teo, C.L. Kane, Phys. Rev. B 89, 085101 (2014)

    ADS  Article  Google Scholar 

  36. 36.

    Y.M. Lu, A. Vishwanath, Phys. Rev. B 86, 125119 (2012)

    ADS  Article  Google Scholar 

  37. 37.

    E. Sagi, Y. Oreg, A. Stern, B.I. Halperin, Phys. Rev. B 91, 245144 (2015)

    ADS  Article  Google Scholar 

  38. 38.

    R.A. Santos, C.W. Huang, Y. Gefen, D.B. Gutman, Phys. Rev. B 91, 205141 (2015)

    ADS  Article  Google Scholar 

  39. 39.

    D.F. Mross, J. Alicea, O.I. Motrunich, Phys. Rev. X 7, 041016 (2017)

    Google Scholar 

  40. 40.

    Y. Fuji, A. Furusaki, Phys. Rev. B 99, 035130 (2019)

    ADS  Article  Google Scholar 

  41. 41.

    Y. Imamura, K. Totsuka, T.H. Hansson, https://arXiv:1904.10404 (2018)

  42. 42.

    T. Neupert, C. Chamon, C. Mudry, R. Thomale, Phys. Rev. B 90, 205101 (2014)

    ADS  Article  Google Scholar 

  43. 43.

    J. Klinovaja, D. Loss, Phys. Rev. Lett. 111, 196401 (2013)

    ADS  Article  Google Scholar 

  44. 44.

    J. Klinovaja, Y. Tserkovnyak, Phys. Rev. B 90, 115426 (2014)

    ADS  Article  Google Scholar 

  45. 45.

    E. Sagi, Y. Oreg, Phys. Rev. B 90, 201102 (2014)

    ADS  Article  Google Scholar 

  46. 46.

    T. Meng, E. Sela, Phys. Rev. B 90, 235425 (2014)

    ADS  Article  Google Scholar 

  47. 47.

    J. Klinovaja, D. Loss, Eur. Phys. J. B 87, 171 (2014)

    ADS  Article  Google Scholar 

  48. 48.

    A. Vaezi, M. Barkeshli, Phys. Rev. Lett. 113, 236804 (2014)

    ADS  Article  Google Scholar 

  49. 49.

    T. Meng, P. Stano, J. Klinovaja, D. Loss, Eur. Phys. J. B 87, 203 (2014)

    ADS  Article  Google Scholar 

  50. 50.

    J. Klinovaja, Y. Tserkovnyak, D. Loss, Phys. Rev. B 91, 085426 (2015)

    ADS  Article  Google Scholar 

  51. 51.

    M. Barkeshli, M. Mulligan, M.P.A. Fisher, Phys. Rev. B 92, 165125 (2015)

    ADS  Article  Google Scholar 

  52. 52.

    J. Cano, T.L. Hughes, M. Mulligan, Phys. Rev. B 92, 075104 (2015)

    ADS  Article  Google Scholar 

  53. 53.

    J. Klinovaja, P. Stano, D. Loss, Phys. Rev. Lett. 116, 176401 (2016)

    ADS  Article  Google Scholar 

  54. 54.

    M. Mulligan, S. Raghu, M.P.A. Fisher, Phys. Rev. B 94, 075101 (2016)

    ADS  Article  Google Scholar 

  55. 55.

    Y. Fuji, P. Lecheminant, Phys. Rev. B 95, 125130 (2017)

    ADS  Article  Google Scholar 

  56. 56.

    C.A. Hernaski, P.R. Gomes, J. High Energy Phys. 2017, 21 (2017)

    Article  Google Scholar 

  57. 57.

    C.L. Kane, A. Stern, Phys. Rev. B 98, 085302 (2018)

    ADS  Article  Google Scholar 

  58. 58.

    M. Thakurathi, J. Klinovaja, D. Loss, Phys. Rev. B 98, 245404 (2018)

    ADS  Article  Google Scholar 

  59. 59.

    A. Sirota, S. Sahoo, G.Y. Cho, J.C.Y. Teo, Phys. Rev. B 99, 245117 (2019)

    ADS  Article  Google Scholar 

  60. 60.

    R.W. Bomantara, L. Zhou, J. Pan, J. Gong, Phys. Rev. B 99, 045441 (2019)

    ADS  Article  Google Scholar 

  61. 61.

    C.E. Bardyn, M. Filippone, T. Giamarchi, Phys. Rev. B 99, 035150 (2019)

    ADS  Article  Google Scholar 

  62. 62.

    W.B. Fontana, P.R.S. Gomes, C.A. Hernaski, Phys. Rev. B 99, 201113 (2019)

    ADS  Article  Google Scholar 

  63. 63.

    O.A. Starykh, R.R.P. Singh, G.C. Levine, Phys. Rev. Lett. 88, 167203 (2002)

    ADS  Article  Google Scholar 

  64. 64.

    A.A. Nersesyan, A.M. Tsvelik, Phys. Rev. B 67, 024422 (2003)

    ADS  Article  Google Scholar 

  65. 65.

    T. Meng, T. Neupert, M. Greiter, R. Thomale, Phys. Rev. B 91, 241106 (2015)

    ADS  Article  Google Scholar 

  66. 66.

    G. Gorohovsky, R.G. Pereira, E. Sela, Phys. Rev. B 91, 245139 (2015)

    ADS  Article  Google Scholar 

  67. 67.

    P.H. Huang, J.H. Chen, P.R.S. Gomes, T. Neupert, C. Chamon, C. Mudry, Phys. Rev. B 93, 205123 (2016)

    ADS  Article  Google Scholar 

  68. 68.

    Y. Fuji, Y.C. He, S. Bhattacharjee, F. Pollmann, Phys. Rev. B 93, 195143 (2016)

    ADS  Article  Google Scholar 

  69. 69.

    A.A. Patel, D. Chowdhury, Phys. Rev. B 94, 195130 (2016)

    ADS  Article  Google Scholar 

  70. 70.

    D. Hill, S.K. Kim, Y. Tserkovnyak, Phys. Rev. B 95, 180405 (2017)

    ADS  Article  Google Scholar 

  71. 71.

    P.H. Huang, J.H. Chen, A.E. Feiguin, C. Chamon, C. Mudry, Phys. Rev. B 95, 144413 (2017)

    ADS  Article  Google Scholar 

  72. 72.

    P. Lecheminant, A.M. Tsvelik, Phys. Rev. B 95, 140406 (2017)

    ADS  Article  Google Scholar 

  73. 73.

    J.H. Chen, C. Mudry, C. Chamon, A.M. Tsvelik, Phys. Rev. B 96, 224420 (2017)

    ADS  Article  Google Scholar 

  74. 74.

    R.G. Pereira, S. Bieri, SciPost Phys. 4, 004 (2018)

    ADS  Article  Google Scholar 

  75. 75.

    J.H. Chen, C. Mudry, C. Chamon, A.M. Tsvelik, Phys. Rev. B 99, 184445 (2019)

    ADS  Article  Google Scholar 

  76. 76.

    R.S.K. Mong et al., Phys. Rev. X 4, 011036 (2014)

    Google Scholar 

  77. 77.

    A. Vaezi, Phys. Rev. X 4, 031009 (2014)

    Google Scholar 

  78. 78.

    I. Seroussi, E. Berg, Y. Oreg, Phys. Rev. B 89, 104523 (2014)

    ADS  Article  Google Scholar 

  79. 79.

    S. Sahoo, Z. Zhang, J.C.Y. Teo, Phys. Rev. B 94, 165142 (2016)

    ADS  Article  Google Scholar 

  80. 80.

    E. Sagi, A. Haim, E. Berg, F. von Oppen, Y. Oreg, Phys. Rev. B 96, 235144 (2017)

    ADS  Article  Google Scholar 

  81. 81.

    C.L. Kane, A. Stern, B.I. Halperin, Phys. Rev. X 7, 031009 (2017)

    Google Scholar 

  82. 82.

    M.J. Park, S. Raza, M.J. Gilbert, J.C.Y. Teo, Phys. Rev. B 98, 184514 (2018)

    ADS  Article  Google Scholar 

  83. 83.

    K. Laubscher, D. Loss, J. Klinovaja, https://arXiv:1905.00885 (2019)

  84. 84.

    Y. Oreg, E. Sela, A. Stern, Phys. Rev. B 89, 115402 (2014)

    ADS  Article  Google Scholar 

  85. 85.

    T. Meng, L. Fritz, D. Schuricht, D. Loss, Phys. Rev. B 89, 045111 (2014)

    ADS  Article  Google Scholar 

  86. 86.

    F. Grusdt, M. Höning, Phys. Rev. A 90, 053623 (2014)

    ADS  Article  Google Scholar 

  87. 87.

    E. Cornfeld, I. Neder, E. Sela, Phys. Rev. B 91, 115427 (2015)

    ADS  Article  Google Scholar 

  88. 88.

    F. Cavaliere, F.M. Gambetta, S. Barbarino, M. Sassetti, Phys. Rev. B 92, 235128 (2015)

    ADS  Article  Google Scholar 

  89. 89.

    E. Cornfeld, E. Sela, Phys. Rev. B 92, 115446 (2015)

    ADS  Article  Google Scholar 

  90. 90.

    S. Barbarino, L. Taddia, D. Rossini, L. Mazza, R. Fazio, Nat. Commun. 6, 8134 (2015)

    ADS  Article  Google Scholar 

  91. 91.

    T.S. Zeng, C. Wang, H. Zhai, Phys. Rev. Lett. 115, 095302 (2015)

    ADS  Article  Google Scholar 

  92. 92.

    A. Petrescu, K. Le Hur, Phys. Rev. B 91, 054520 (2015)

    ADS  Article  Google Scholar 

  93. 93.

    M. Calvanese Strinati, E. Cornfeld, D. Rossini, S. Barbarino, M. Dalmonte, R. Fazio, E. Sela, L. Mazza, Phys. Rev. X 7, 021033 (2017)

    Google Scholar 

  94. 94.

    J.C. Budich, A. Elben, M. Łacki, A. Sterdyniak, M.A. Baranov, P. Zoller, Phys. Rev. A 95, 043632 (2017)

    ADS  Article  Google Scholar 

  95. 95.

    A. Petrescu, M. Piraud, G. Roux, I.P. McCulloch, K. Le Hur, Phys. Rev. B 96, 014524 (2017)

    ADS  Article  Google Scholar 

  96. 96.

    P.P. Aseev, D. Loss, J. Klinovaja, Phys. Rev. B 98, 045416 (2018)

    ADS  Article  Google Scholar 

  97. 97.

    A. Haller, M. Rizzi, M. Burrello, New J. Phys. 20, 053007 (2018)

    ADS  Article  Google Scholar 

  98. 98.

    M. Filippone, C.E. Bardyn, T. Giamarchi, Phys. Rev. B 97, 201408 (2018)

    ADS  Article  Google Scholar 

  99. 99.

    G. Shavit, Y. Oreg, Phys. Rev. Lett. 123, 036803 (2019)

    ADS  Article  Google Scholar 

  100. 100.

    M. Calvanese Strinati, S. Sahoo, K. Shtengel, E. Sela, Phys. Rev. B 99, 245101 (2019)

    ADS  Article  Google Scholar 

  101. 101.

    N.H. Lindner, E. Berg, G. Refael, A. Stern, Phys. Rev. X 2, 041002 (2012)

    Google Scholar 

  102. 102.

    D.J. Clarke, J. Alicea, K. Shtengel, Nat. Commun. 4, 1348 (2013)

    ADS  Article  Google Scholar 

  103. 103.

    M. Barkeshli, C.M. Jian, X.L. Qi, Phys. Rev. B 87, 045130 (2013)

    ADS  Article  Google Scholar 

  104. 104.

    J. Klinovaja, A. Yacoby, D. Loss, Phys. Rev. B 90, 155447 (2014)

    ADS  Article  Google Scholar 

  105. 105.

    J. Klinovaja, D. Loss, Phys. Rev. B 90, 045118 (2014)

    ADS  Article  Google Scholar 

  106. 106.

    M. Barkeshli, X.L. Qi, Phys. Rev. X 4, 041035 (2014)

    Google Scholar 

  107. 107.

    F. Zhang, C.L. Kane, Phys. Rev. Lett. 113, 036401 (2014)

    ADS  Article  Google Scholar 

  108. 108.

    J. Klinovaja, D. Loss, Phys. Rev. Lett. 112, 246403 (2014)

    ADS  Article  Google Scholar 

  109. 109.

    M.F. Maghrebi, S. Ganeshan, D.J. Clarke, A.V. Gorshkov, J.D. Sau, Phys. Rev. Lett. 115, 065301 (2015)

    ADS  Article  Google Scholar 

  110. 110.

    C.P. Orth, R.P. Tiwari, T. Meng, T.L. Schmidt, Phys. Rev. B 91, 081406 (2015)

    ADS  Article  Google Scholar 

  111. 111.

    J. Klinovaja, D. Loss, Phys. Rev. B 92, 121410 (2015)

    ADS  Article  Google Scholar 

  112. 112.

    C. Chen, F.J. Burnell, Phys. Rev. Lett. 116, 106405 (2016)

    ADS  Article  Google Scholar 

  113. 113.

    C.J. Pedder, T. Meng, R.P. Tiwari, T.L. Schmidt, Phys. Rev. B 94, 245414 (2016)

    ADS  Article  Google Scholar 

  114. 114.

    N. Traverso Ziani, C. Fleckenstein, G. Dolcetto, B. Trauzettel, Phys. Rev. B 95, 205418 (2017)

    ADS  Article  Google Scholar 

  115. 115.

    H. Ebisu, E. Sagi, Y. Tanaka, Y. Oreg, Phys. Rev. B 95, 075111 (2017)

    ADS  Article  Google Scholar 

  116. 116.

    C.J. Pedder, T. Meng, R.P. Tiwari, T.L. Schmidt, Phys. Rev. B 96, 165429 (2017)

    ADS  Article  Google Scholar 

  117. 117.

    Y. Alavirad, D. Clarke, A. Nag, J.D. Sau, Phys. Rev. Lett. 119, 217701 (2017)

    ADS  Article  Google Scholar 

  118. 118.

    Y. Vinkler-Aviv, P.W. Brouwer, F. von Oppen, Phys. Rev. B 96, 195421 (2017)

    Article  Google Scholar 

  119. 119.

    L.H. Santos, T.L. Hughes, Phys. Rev. Lett. 118, 136801 (2017)

    ADS  Article  Google Scholar 

  120. 120.

    M.S. Vaezi, A. Vaezi, https://arXiv:1706.01192 (2017)

  121. 121.

    A. Calzona, T. Meng, M. Sassetti, T.L. Schmidt, Phys. Rev. B 98, 201110 (2018)

    ADS  Article  Google Scholar 

  122. 122.

    C. Fleckenstein, N.T. Ziani, B. Trauzettel, Phys. Rev. Lett. 122, 066801 (2019)

    ADS  Article  Google Scholar 

  123. 123.

    J. Alicea, O.I. Motrunich, G. Refael, M.P.A. Fisher, Phys. Rev. Lett. 103, 256403 (2009)

    ADS  Article  Google Scholar 

  124. 124.

    F.A. Bais, J.K. Slingerland, Phys. Rev. B 79, 045316 (2009)

    ADS  Article  Google Scholar 

  125. 125.

    A. Vishwanath, T. Senthil, Phys. Rev. X 3, 011016 (2013)

    Google Scholar 

  126. 126.

    M.M. Vazifeh, Europhys. Lett. 102, 67011 (2013)

    ADS  Article  Google Scholar 

  127. 127.

    C.M. Jian, X.L. Qi, Phys. Rev. X 4, 041043 (2014)

    Google Scholar 

  128. 128.

    H. Obuse, S. Ryu, A. Furusaki, C. Mudry, Phys. Rev. B 89, 155315 (2014)

    ADS  Article  Google Scholar 

  129. 129.

    E. Sagi, Y. Oreg, Phys. Rev. B 92, 195137 (2015)

    ADS  Article  Google Scholar 

  130. 130.

    T. Meng, Phys. Rev. B 92, 115152 (2015)

    ADS  Article  Google Scholar 

  131. 131.

    H. Isobe, L. Fu, Phys. Rev. B 92, 081304 (2015)

    ADS  Article  Google Scholar 

  132. 132.

    D.F. Mross, A. Essin, J. Alicea, Phys. Rev. X 5, 011011 (2015)

    Google Scholar 

  133. 133.

    T. Meng, A.G. Grushin, K. Shtengel, J.H. Bardarson, Phys. Rev. B 94, 155136 (2016)

    ADS  Article  Google Scholar 

  134. 134.

    D.F. Mross, J. Alicea, O.I. Motrunich, Phys. Rev. Lett. 117, 136802 (2016)

    ADS  Article  Google Scholar 

  135. 135.

    D.F. Mross, A. Essin, J. Alicea, A. Stern, Phys. Rev. Lett. 116, 036803 (2016)

    ADS  Article  Google Scholar 

  136. 136.

    L. Trifunovic, D. Loss, J. Klinovaja, Phys. Rev. B 93, 205406 (2016)

    ADS  Article  Google Scholar 

  137. 137.

    T. Iadecola, T. Neupert, C. Chamon, C. Mudry, Phys. Rev. B 93, 195136 (2016)

    ADS  Article  Google Scholar 

  138. 138.

    T. Iadecola, T. Neupert, C. Chamon, C. Mudry, Phys. Rev. B 99, 245138 (2019)

    ADS  Article  Google Scholar 

  139. 139.

    F. Lu, B. Shi, Y.M. Lu, N. J. Phys. 19, 073002 (2017)

    Article  Google Scholar 

  140. 140.

    Y. You, https://arXiv:1704.03463 (2017)

  141. 141.

    Y. Volpez, D. Loss, J. Klinovaja, Phys. Rev. B 96, 085422 (2017)

    ADS  Article  Google Scholar 

  142. 142.

    S. Hong, L. Fu, https://arXiv:1707.02594 (2017)

  143. 143.

    M. Cheng, Phys. Rev. Lett. 120, 036801 (2018)

    ADS  Article  Google Scholar 

  144. 144.

    B. Han, J.C.Y. Teo, Phys. Rev. B 99, 235102 (2019)

    ADS  Article  Google Scholar 

  145. 145.

    E. Sagi, A. Stern, D.F. Mross, Phys. Rev. B 98, 201111 (2018)

    ADS  Article  Google Scholar 

  146. 146.

    Y. Fuji, A. Furusaki, Phys. Rev. B 99, 241107 (2019)

    ADS  Article  Google Scholar 

  147. 147.

    V. Kalmeyer, R.B. Laughlin, Phys. Rev. B 39, 11879 (1989)

    ADS  Article  Google Scholar 

  148. 148.

    X.G. Wen, F. Wilczek, A. Zee, Phys. Rev. B 39, 11413 (1989)

    ADS  Article  Google Scholar 

  149. 149.

    R.B. Laughlin, Z. Zou, Phys. Rev. B 41, 664 (1990)

    ADS  Article  Google Scholar 

  150. 150.

    C. Herring, Phys. Rev. 52, 365 (1937)

    ADS  Article  Google Scholar 

  151. 151.

    G. Volovik,The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003)

  152. 152.

    X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Phys. Rev. B 83, 205101 (2011)

    ADS  Article  Google Scholar 

  153. 153.

    A.M. Turner, A. Vishwanath, https://arXiv:1301.0330 (2013)

  154. 154.

    B. Yan, C. Felser, Annu. Rev. Condens. Matter Phys. 8, 337 (2017)

    ADS  Article  Google Scholar 

  155. 155.

    A. Burkov, Annu. Rev. Condens. Matter Phys. 9, 359 (2018)

    ADS  Article  Google Scholar 

  156. 156.

    N.P. Armitage, E.J. Mele, A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018)

    ADS  Article  Google Scholar 

  157. 157.

    H. Nielsen, M. Ninomiya, Phys. Lett. B 105, 219 (1981)

    ADS  Article  Google Scholar 

  158. 158.

    H. Nielsen, M. Ninomiya, Nucl. Phys. B 185, 20 (1981)

    ADS  Article  Google Scholar 

  159. 159.

    H. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981)

    ADS  Article  Google Scholar 

  160. 160.

    H. Nielsen, M. Ninomiya, Phys. Lett. B 130, 389 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  161. 161.

    T. Meng, J.C. Budich, Phys. Rev. Lett. 122, 046402 (2019)

    ADS  Article  Google Scholar 

  162. 162.

    S.C. Zhang, J. Hu, Science 294, 823 (2001)

    ADS  Article  Google Scholar 

  163. 163.

    D. Karabali, V. Nair, Nucl. Phys. B 641, 533 (2002)

    ADS  Article  Google Scholar 

  164. 164.

    J. Fröhlich, B. Perdini, inMathematical Physics 2000, edited by A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (Imperial College Press, 2000), pp. 9–47

  165. 165.

    O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, Phys. Rev. Lett. 108, 133001 (2012)

    ADS  Article  Google Scholar 

  166. 166.

    N. Goldman, J.C. Budich, P. Zoller, Nat. Phys. 12, 639 (2016)

    Article  Google Scholar 

  167. 167.

    T. Ozawa, H.M. Price, Nat. Rev. Phys. 1, 349 (2019)

    Article  Google Scholar 

  168. 168.

    H.M. Price, O. Zilberberg, T. Ozawa, I. Carusotto, N. Goldman, Phys. Rev. Lett. 115, 195303 (2015)

    ADS  Article  Google Scholar 

  169. 169.

    M. Lohse, C. Schweizer, H.M. Price, O. Zilberberg, I. Bloch, Nature 553, 55 (2018)

    ADS  Article  Google Scholar 

  170. 170.

    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    ADS  Article  Google Scholar 

  171. 171.

    I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)

    ADS  Article  Google Scholar 

  172. 172.

    A.Y. Kitaev, Physics-Uspekhi 44, 131 (2001)

    ADS  Article  Google Scholar 

Download references

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Meng, T. Coupled-wire constructions: a Luttinger liquid approach to topology. Eur. Phys. J. Spec. Top. 229, 527–543 (2020). https://doi.org/10.1140/epjst/e2019-900095-5

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