1932

Abstract

Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)IrO iridates and RuCl. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.

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2018-03-10
2024-05-21
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Literature Cited

  1. Anderson PW. 1.  1973. Mater. Res. Bull. 8:2153–60
  2. Moessner R, Sondhi SL. 2.  2001. Phys. Rev. Lett. 86:1881–84
  3. Wen X-G. 3.  2004. Quantum Field Theory of Many-Body Systems Oxford, UK: Oxford Univ. Press
  4. Lacroix C, Mendels P, Mila F. 4.  2011. Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer Series in Solid-State Sciences) Berlin/Heidelberg: Springer
  5. Lee PA. 5.  2008. 32158941306–7
  6. Leon B. 6.  2010. Nature 464:7286199–208
  7. Wen X-G. 7.  2013. ISRN Condens. Matter Phys. 2013:198710
  8. Jiang H-C, Wang Z, Balents L. 8.  2012. Nat. Phys. 8:12902–5
  9. Kitaev A. 9.  2006. Ann. Phys. 321:12–111
  10. Khaliullin G. 10.  2005. Prog. Theor. Phys. Suppl. 160:155
  11. Jackeli G, Khaliullin G. 11.  2009. Phys. Rev. Lett. 102:017205
  12. Okamoto Y, Nohara M, Aruga-Katori H, Takagi H. 12.  2007. Phys. Rev. Lett. 99:137207
  13. Singh Y, Gegenwart P. 13.  2010. Phys. Rev. B 82:064412
  14. Singh Y, Manni S, Reuther J, Berlijn T, Thomale R. 14.  et al. 2012. Phys. Rev. Lett. 108:127203
  15. Modic KA, Smidt TE, Kimchi I, Breznay NP, Biffin A. 15.  et al. 2014. Nat. Commun. 5:4203
  16. Plumb KW, Clancy JP, Sandilands LJ, Shankar VV, Hu YF. 16.  et al. 2014. Phys. Rev. B 90:041112
  17. Takayama T, Kato A, Dinnebier R, Nuss J, Kono H. 17.  et al. 2015. Phys. Rev. Lett. 114:077202
  18. Yamada MG, Fujita H, Oshikawa M. 18.  2017. Phys. Rev. Lett. 119:057202
  19. Duan L-M, Demler E, Lukin MD. 19.  2003. Phys. Rev. Lett. 91:090402
  20. Liu X, Berlijn T, Yin W-G, Ku W, Tsvelik A. 20.  et al. 2011. Phys. Rev. B 83:220403
  21. Ye F, Chi S, Cao H, Chakoumakos BC, Fernandez-Baca JA. 21.  et al. 2012. Phys. Rev. B 85:180403
  22. Choi SK, Coldea R, Kolmogorov AN, Lancaster T, Mazin II. 22.  et al. 2012. Phys. Rev. Lett. 108:127204
  23. Biffin A, Johnson RD, Choi S, Freund F, Manni S. 23.  et al. 2014. Phys. Rev. B 90:205116
  24. Biffin A, Johnson RD, Kimchi I, Morris R, Bombardi A. 24.  et al. 2014. Phys. Rev. Lett. 113:197201
  25. Sears JA, Songvilay M, Plumb KW, Clancy JP, Qiu Y. 25.  et al. 2015. Phys. Rev. B 91:144420
  26. Williams SC, Johnson RD, Freund F, Choi S, Jesche A. 26.  et al. 2016. Phys. Rev. B 93:195158
  27. Chun SH, Kim J-W, Kim J, Zheng H, Stoumpos CC. 27.  et al. 2015. Nat. Phys. 11:462–66
  28. Breznay NP, Ruiz A, Frano A, Bi W, Birgeneau RJ. 28.  et al. 2017. Phys. Rev. B 96:020402R)
  29. Banerjee A, Bridges CA, Yan J-Q, Aczel AA, Li L. 29.  et al. 2016. Nat. Mater. 15:733–40
  30. Banerjee A, Yan J, Knolle J, Bridges CA, Stone MB. 30.  et al. 2017. Science 356:63421055–59
  31. Sandilands LJ, Tian Y, Reijnders AA, Kim H-S, Plumb KW. 31.  et al. 2016. Phys. Rev. B 93:075144
  32. Nasu J, Knolle J, Kovrizhin DL, Motome Y, Moessner R. 32.  2016. Nat. Phys. 12:912–15
  33. You Y-Z, Kimchi I, Vishwanath A. 33.  2012. Phys. Rev. B 86:085145
  34. Hyart T, Wright AR, Khaliullin G, Rosenow B. 34.  2012. Phys. Rev. B 85:140510
  35. Okamoto S. 35.  2013. Phys. Rev. B 87:064508
  36. Halász GB, Chalker JT, Moessner R. 36.  2014. Phys. Rev. B 90:035145
  37. Yao H, Kivelson SA. 37.  2007. Phys. Rev. Lett. 99:247203
  38. Yang S, Zhou DL, Sun CP. 38.  2007. Phys. Rev. B 76:180404
  39. Tieyan Si, Yue Yu. 39.  2008. Nucl. Phys. B 803:3428–49
  40. Mandal S, Surendran N. 40.  2009. Phys. Rev. B 79:024426
  41. Kamfor M, Dusuel S, Vidal J, Schmidt KP. 41.  2010. J. Stat. Mech.: Theory Exp. 2010:08P08010
  42. Hermanns M, Trebst S. 42.  2014. Phys. Rev. B 89:235102
  43. Hermanns M, O'Brien K, Trebst S. 43.  2015. Phys. Rev. Lett. 114:157202
  44. Hermanns M, Trebst S, Rosch A. 44.  2015. Phys. Rev. Lett. 115:177205
  45. O'Brien K, Hermanns M, Trebst S. 45.  2016. Phys. Rev. B 93:085101
  46. Rachel S, Fritz L, Vojta M. 46.  2016. Phys. Rev. Lett. 116:167201
  47. Kugel' KI, Khomskii DI. 47.  1982. Sov. Phys. Uspekhi 25:4231
  48. Chandra S, Ramola K, Dhar D. 48.  2010. Phys. Rev. E 82:031113
  49. Sela E, Jiang H-C, Gerlach MH, Trebst S. 49.  2014. Phys. Rev. B 90:035113
  50. Henley CL. 50.  2010. Annu. Rev. Condens. Matter Phys. 1:179–210
  51. Wen X-G. 51.  2002. Phys. Rev. B 65:165113
  52. Kitaev A, Laumann C. 52.  2009. arXiv0904.2771
  53. Lieb EH. 53.  1994. Phys. Rev. Lett. 73:2158–61
  54. Pedrocchi FL, Chesi S, Loss D. 54.  2011. Phys. Rev. B 84:165414
  55. Zschocke F, Vojta M. 55.  2015. Phys. Rev. B 92:014403
  56. Kitaev AYu. 56.  2003. Ann. Phys. 303:2–30
  57. Hamma A, Zanardi P, Wen X-G. 57.  2005. Phys. Rev. B 72:035307
  58. Lai H-H, Motrunich OI. 58.  2011. Phys. Rev. B 84:085141
  59. Schaffer R, Lee EK-H, Lu Y-M, Kim YB. 59.  2015. Phys. Rev. Lett. 114:116803
  60. Schnyder AP, Ryu S, Furusaki A, Ludwig AWW. 60.  2008. Phys. Rev. B 78:195125
  61. Kitaev A. 61.  2009. Advances in Theoretical Physics: Landau Memorial Conf V Lebedev, M Feigel'man AIP Conf. Proc 1134122–30 Melville, NY: AIP
  62. Chiu C-K, Teo JCY, Schnyder AP, Ryu S. 62.  2016. Rev. Mod. Phys. 88:035005
  63. Yamada MG, Dwivedi V, Hermanns M. 63.  2017. Phys. Rev. B 96155107
  64. Lee EK-H, Schaffer R, Bhattacharjee S, Kim YB. 64.  2014. Phys. Rev. B 89:045117
  65. Pachos JK. 65.  2007. Ann. Phys. 322:61254–64
  66. Senthil T, Fisher MPA. 66.  2000. Phys. Rev. B 62:7850–81
  67. Nasu J, Udagawa M, Motome Y. 67.  2014. Phys. Rev. Lett. 113:197205
  68. Kamiya Y, Kato Y, Nasu J, Motome Y. 68.  2015. Phys. Rev. B 92:100403
  69. Kimchi I, Analytis JG, Vishwanath A. 69.  2014. Phys. Rev. B 90:205126
  70. Nasu J, Udagawa M, Motome Y. 70.  2015. Phys. Rev. B 92:115122
  71. Yamaji Y, Suzuki T, Yamada T, Suga S-I, Kawashima N, Imada M. 71.  2016. Phys. Rev. B 93:174425
  72. Chaloupka J, Jackeli G, Khaliullin G. 72.  2010. Phys. Rev. Lett. 105:027204
  73. Kimchi I, Coldea R, Vishwanath A. 73.  2015. Phys. Rev. B 91:245134
  74. Rau JG, Lee EK-H, Kee H-Y. 74.  2014. Phys. Rev. Lett. 112:077204
  75. Chaloupka J, Khaliullin G. 75.  2015. Phys. Rev. B 92:024413
  76. Foyevtsova K, Jeschke HO, Mazin II, Khomskii DI, Valentí R. 76.  2013. Phys. Rev. B 88:035107
  77. Mazin II, Manni S, Foyevtsova K, Jeschke HO, Gegenwart P, Valentí R. 77.  2013. Phys. Rev. B 88:035115
  78. Winter SM, Li Y, Jeschke HO, Valentí R. 78.  2016. Phys. Rev. B 93:214431
  79. Foyevtsova K, Jeschke HO, Mazin II, Khomskii DI, Valentí R. 79.  2013. Phys. Rev. B 88:035107
  80. Kim H-S, Vijay Shankar V, Catuneanu A, Kee H-Y. 80.  2015. Phys. Rev. B 91:241110
  81. Jackeli G, Avella A. 81.  2015. Phys. Rev. B 92:184416
  82. Reuther J, Thomale R, Rachel S. 82.  2012. Phys. Rev. B 86:155127
  83. Rousochatzakis I, Rössler UK, van den Brink J, Daghofer M. 83.  2016. Phys. Rev. B 93:104417
  84. Becker M, Hermanns M, Bauer B, Garst M, Trebst S. 84.  2015. Phys. Rev. B 91:155135
  85. Lee SB, Lee EK-H, Paramekanti A, Kim YB. 85.  2014. Phys. Rev. B 89:014424
  86. Lee EK-H, Kim YB. 86.  2015. Phys. Rev. B 91:064407
  87. Kimchi I, Vishwanath A. 87.  2014. Phys. Rev. B 89:014414
  88. Khaliullin G. 88.  2001. Phys. Rev. B 64:212405
  89. Yao H, Qi X-L. 89.  2010. Phys. Rev. Lett. 105:080501
  90. Chen H-D, Nussinov Z. 90.  2008. J. Phys. A: Math. Theor. 41:7075001
  91. Lahtinen V, Pachos JK. 91.  2009. N. J. Phys. 11:9093027
  92. Feng X-Y, Zhang G-M, Xiang T. 92.  2007. Phys. Rev. Lett. 98:087204
  93. Baskaran G, Mandal S, Shankar R. 93.  2007. Phys. Rev. Lett. 98:247201
  94. Tikhonov KS, Feigel'man MV, AYu Kitaev. 94.  2011. Phys. Rev. Lett. 106:067203
  95. Mandal S, Bhattacharjee S, Sengupta K, Shankar R, Baskaran G. 95.  2011. Phys. Rev. B 84:155121
  96. Lai H-H, Motrunich OI. 96.  2011. Phys. Rev. B 83:155104
  97. Yang S, Gu S-J, Sun C-P, Lin H-Q. 97.  2008. Phys. Rev. A 78:012304
  98. Nozieres P, De Dominicis CT. 98.  1969. Phys. Rev. 178:1097–107
  99. Knolle J, Kovrizhin DL, Chalker JT, Moessner R. 99.  2014. Phys. Rev. Lett. 112:207203
  100. Knolle J, Kovrizhin DL, Chalker JT, Moessner R. 100.  2015. Phys. Rev. B 92:115127
  101. Knolle J. 101.  2016. Dynamics of a Quantum Spin Liquid (Springer Theses) Cham/Heidelberg/NewYork/Dordrecht/London: Springer Intl. Publ.
  102. Smith A, Knolle J, Kovrizhin DL, Chalker JT, Moessner R. 102.  2015. Phys. Rev. B 92:180408
  103. Smith A, Knolle J, Kovrizhin DL, Chalker JT, Moessner R. 103.  2016. Phys. Rev. B 93:235146
  104. Knolle J, Chern G-W, Kovrizhin DL, Moessner R, Perkins NB. 104.  2014. Phys. Rev. Lett. 113:187201
  105. Fleury PA, Loudon R. 105.  1968. Phys. Rev. 166:514–30
  106. Perreault B, Knolle J, Perkins NB, Burnell FJ. 106.  2016. Phys. Rev. B 94:104427
  107. Perreault B, Knolle J, Perkins NB, Burnell FJ. 107.  2016. Phys. Rev. B 94:060408
  108. Perreault B, Rachel S, Burnell FJ, Knolle J. 108.  2017. Phys. Rev. B 95:184429
  109. Perreault B, Knolle J, Perkins NB, Burnell FJ. 109.  2015. Phys. Rev. B 92:094439
  110. Halász GB, Perkins NB, van den Brink J. 110.  2016. Phys. Rev. Lett. 117:127203
  111. Song X-Y, You Y-Z, Balents L. 111.  2016. Phys. Rev. Lett. 117:037209
  112. Jiang H-C, Gu Z-C, Qi X-L, Trebst S. 112.  2011. Phys. Rev. B 83:245104
  113. Chaloupka J, Jackeli G, Khaliullin G. 113.  2013. Phys. Rev. Lett. 110:097204
  114. Shinjo K, Sota S, Tohyama T. 114.  2015. Phys. Rev. B 91:054401
  115. Yoshitake J, Nasu J, Motome Y. 115.  2016. Phys. Rev. Lett. 117:157203
  116. Willans AJ, Chalker JT, Moessner R. 116.  2010. Phys. Rev. Lett. 104:237203
  117. Willans AJ, Chalker JT, Moessner R. 117.  2011. Phys. Rev. B 84:115146
  118. Dhochak K, Shankar R, Tripathi V. 118.  2010. Phys. Rev. Lett. 105:117201
  119. Vojta M, Mitchell AK, Zschocke F. 119.  2016. Phys. Rev. Lett. 117:037202
  120. Sreejith GJ, Bhattacharjee S, Moessner R. 120.  2016. Phys. Rev. B 93:064433
  121. Halász GB, Chalker JT. 121.  2016. Phys. Rev. B 94:235105
  122. Gohlke M, Verresen R, Moessner R, Pollmann F. 122.  2017. arXiv1701.04678
  123. Kimchi I, Coldea R. 123.  2016. Phys. Rev. B 94:201110
  124. Khaliullin G, Okamoto S. 124.  2002. Phys. Rev. Lett. 89:167201
  125. Winter SM, Riedl K, Honecker A, Valenti R. 125.  2017. arXiv1702.08466
  126. Witczak-Krempa W, Chen G, Kim YB, Balents L. 126.  2014. Annu. Rev. Condens. Matter Phys. 5:57–82
  127. Rau JG, Lee EK-H, Kee H-Y. 127.  2016. Annu. Rev. Condens. Matter Phys. 7:195–221
  128. Zhou Y, Kanoda K, Ng T-K. 128.  2017. Rev. Mod. Phys. 89:025003
  129. Savary L, Balents L. 129.  2017. Rep. Prog. Phys. 80:1016502
  130. Trebst S. 130.  2017. Kitaev Materials Lect. Notes 48th IFF Spring Sch. “Topol. Matter – Topol. Insul. Skyrmions Majoranas,” Forschungszentrum Jülich, Jülick, Germ., Mar. 27–Apr. 7. arXiv:1701.07056 [Google Scholar]
  131. Obradors X, Labarta A, Isalgu A, Tejada J, Rodriguez J, Pernet M. 131.  1988. Solid State Commun 65:3189–92
  132. Ramirez AP. 132.  1994. Annu. Rev. Mater. Sci. 24:453–80
  133. Reuther J, Thomale R, Trebst S. 133.  2011. Phys. Rev. B 84:100406
  134. Mazin II, Jeschke HO, Foyevtsova K, Valentí R, Khomskii DI. 134.  2012. Phys. Rev. Lett. 109:197201
  135. Kimchi I, You Y-Z. 135.  2011. Phys. Rev. B 84:180407
  136. Sandilands LJ, Tian Y, Plumb KW, Kim Y-J, Burch KS. 136.  2015. Phys. Rev. Lett. 114:147201
  137. Glamazda A, Lemmens P, Do SH, Choi YS, Choi KY. 137.  2016. Nat. Commun. 7:12286
  138. Do S-H, Park S-Y, Yoshitake J, Nasu J, Motome Y. 138.  et al. 2017. arXiv1703.01081
  139. Hirobe D, Sato M, Shiomi Y, Tanaka H, Saitoh E. 139.  2017. Phys. Rev. B 95:241112
  140. Leahy IA, Pocs CA, Siegfried PE, Graf D, Do S-H. 140.  et al. 2017. Phys. Rev. Lett. 118:187203
  141. Yadav R, Bogdanov NA, Katukuri VM, Nishimoto S, van den Brink J, Hozoi L. 141.  2016. Sci. Rep. 6:37925
  142. Tennant DA, Cowley RA, Nagler SE, Tsvelik AM. 142.  1995. Phys. Rev. B 52:13368–80
  143. Mourigal M, Enderle M, Klöpperpieper A, Caux J-S, Stunault A, Røonnow HM. 143.  2013. Nat. Phys. 9:435–41
  144. Takayama T, Takagi H. 144.  2016. Talk presented at APS March Meet., Mar. 14–18 http://meetings.aps.org/link/BAPS.2016.MAR.K2.4 [Google Scholar]
  145. Kubota Y, Tanaka H, Ono T, Narumi Y, Kindo K. 145.  2015. Phys. Rev. B 91:094422
  146. Johnson RD, Williams SC, Haghighirad AA, Singleton J, Zapf V. 146.  et al. 2015. Phys. Rev. B 92:235119
  147. Majumder M, Schmidt M, Rosner H, Tsirlin AA, Yasuoka H, Baenitz M. 147.  2015. Phys. Rev. B 91:180401
  148. Baek S-H, Do S-H, Choi K-Y, Kwon YS, Wolter AUB. 148.  et al. 2017. Phys. Rev. Lett. 119:037201
  149. Modic KA, Ramshaw BJ, Betts JB, Breznay NP, Analytis JG. 149.  et al. 2017. Nat. Commun. 8:108
  150. Ruiz A, Frano A, Breznay NP, Kimchi I, Helm T. 150.  et al. 2017. arXiv1703.02531
  151. Ohrstrom L, Larsson K. 151.  2004. Dalton Trans 2004:347–53
  152. Jiang H-C, Gu Z-C, Qi X-L, Trebst S. 152.  2011. Phys. Rev. B 83:245104
  153. Rousochatzakis I, Reuther J, Thomale R, Rachel S, Perkins NB. 153.  2015. Phys. Rev. X 5:041035
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