Bridging lattice-scale physics and continuum field theory with quantum monte carlo simulations

Annual Review of Condensed Matter Physics

Volumn 4, Issue 1, 2013, Pages 179-215

  Kaul, Ribhu K ^a   Melko, Roger G ^b,c   Sandvik, Anders W ^d  

^a UNIVERSITY OF KENTUCKY   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^d USA   (United States)

Author keywords

fractionalization; quantum criticality; quantum spin liquid; valence bond solid

Indexed keywords

FRACTIONALIZATION; NONMAGNETIC GROUNDSTATES; QUANTUM CRITICALITY; QUANTUM MONTE CARLO METHODS; QUANTUM MONTE CARLO SIMULATIONS; QUANTUM PHASE TRANSITIONS; QUANTUM SPIN LIQUID; VALENCE-BOND SOLIDS;

GROUND STATE; MONTE CARLO METHODS; PARAMAGNETISM; PHASE TRANSITIONS;

QUANTUM ENTANGLEMENT;

EID: 84874925692     PISSN: 19475454     EISSN: 19475462     Source Type: Journal    
DOI: 10.1146/annurev-conmatphys-030212-184215     Document Type: Article

References (239)

1. Sachdev S. 2011. Quantum Phase Transitions. Cambridge, MA: Cambridge Univ. Press
2. Cardy JL. 1988. Finite-Size Scaling. Amsterdam: North Holland
3. Chaikin PM, Lubensky TC. 2000. Principles of Condensed Matter Physics. Cambridge, MA: Cambridge Univ. Press
4. Loh EY, Gubernatis JE, Scalettar RT, White SR, Scalapino DJ, Sugar RL. 1990. Phys. Rev. B 41:9301-7
5. Henelius P, Sandvik AW. 2000. Phys. Rev. B 62:1102-113
6. Nyfeler M, Jiang FJ, Kämpfer F, Wiese UJ. 2008. Phys. Rev. Lett. 100:247206
7. Wen XG. 2003. Phys. Rev. Lett. 90:016803
8. Sandvik AW, Kurkijärvi J. 1991. Phys. Rev. B 43:5950-61
9. Evertz HG, Lana G, Marcu M. 1993. Phys. Rev. Lett. 70:875-79
10. Beard BB, Wiese UJ. 1996. Phys. Rev. Lett. 77:5130-33
11. Prokof'ev NV, Svistunov BV, Tupitsyn IS. 1998. Phys. Lett. A 238:253-57
12. Sandvik AW. 1999. Phys. Rev. B 59:R14157-60
13. Sandvik AW, Evertz HG. 2010. Phys. Rev. B 82:024407
14. Schwandt D, Alet F, Capponi S. 2009. Phys. Rev. Lett. 103:170501
15. De Grandi C, Polkovnikov A, Sandvik AW. 2011. Phys. Rev. B 84:224303
16. Hastings MB, González I, Kallin AB, Melko RG. 2010. Phys. Rev. Lett. 104:157201
17. Melko RG, Kallin AB, Hastings MB. 2010. Phys. Rev. B 82:100409
18. Herbut I. 2007. A Modern Approach to Critical Phenomena. Cambridge, MA: Cambridge Univ. Press
19. Barber MN. 1977. Phys. Rep. 29:2-84
20. Haldane FDM. 1983. Phys. Rev. Lett. 50:1153-56
21. Chakravarty S, Halperin BI, Nelson DR. 1989. Phys. Rev. B 39:2344-71
22. Auerbach A. 1994. Interacting Electrons and Quantum Magnetism. New York/Berlin/Heidelberg: Springer-Verlag
23. Senthil T, Vishwanath A, Balents L, Sachdev S, Fisher MPA. 2004. Science 303:1490-94
24. Sachdev S. 2008. Nat. Phys. 4:173-85
25. Bethte HA. 1931. Z. Phys. 71:205-26
26. Affleck I, Kennedy T, Lieb EH, Tasaki H. 1988. Commun. Math. Phys. 115:477-528
27. Nakano H, Sakai T. 2011. J. Phys. Soc. Jpn. 97:053704
28. Läuchli AM, Sudan J, Sørensen ES. 2011. Phys. Rev. B 83:212401
29. White SR. 1992. Phys. Rev. Lett. 69:2863-66
30. Schollwöck U. 2005. Rev. Mod. Phys. 77:259-315
31. Dagotto E, Rice TM. 1996. Science 271:618-23
32. Sandvik AW, Balents L, Campbell DK. 2004. Phys. Rev. Lett. 92:236401
33. Jeckelmann E. 2002. Phys. Rev. Lett. 89:236401
34. Mund C, Legeza O, Noack RM. 2009. Phys. Rev. B 79:245130
35. Stoudenmire E, White SR. 2012. Annu. Rev. Condens. Matter Phys. 3:111-28
36. Murg V, Verstraete F, Cirac JI. 2009. Phys. Rev. B 79:195119
37. Gu ZC, Levin M, Wen XG. 2008. Phys. Rev. B 78:205116
38. Xie ZY, Jiang HC, Chen QN, Weng ZY, Xiang T. 2009. Phys. Rev. Lett. 103:160601
39. Rommer S, Östlund S. 1997. Phys. Rev. B 55:2164-81
40. Yan S, Huse DA, White SR. 2011. Science 332:1173-76
41. Bauer B, Corboz P, Läuchli AM, Messio L, Penc K, et al. 2012. Phys. Rev. B 85:125116
42. Evertz HG. 1993. Adv. Phys. 52:1-47
43. Sandvik AW. 2010. AIP Conf. Proc. 1297:135-338
44. Zvyagin SA, Wosnitza J, Batista CD, Tsukamoto M, Kawashima N, et al. 2007. Phys. Rev. Lett. 98:047205
45. Rieger H, Young AP. 1994. Phys. Rev. Lett. 72:4141-44
46. Sørensen ES, Wallin M, Girvin SM, Young AP. 1992. Phys. Rev. Lett. 69:828-31
47. Nahum A, Chalker JT, Serna P, Ortuño M, Somoza AM. 2011. Phys. Rev. Lett. 107:110601
48. Suzuki M. 1976. Prog. Theor. Phys. 56:1454-69
49. Fradkin E, Huse DA, Moessner R, Oganesyan V, Sondhi SL. 2004. Phys. Rev. B 69:224415
50. Assaad FF, Evertz HG. 2007. In Computational Many-Particle Physics (Lect. Notes Phys. 739), pp. 277. Berlin/Heidelberg: Springer-Verlag
51. Kashurnikov VA, Prokof'ev NV, Svistunov BV. 2002. Phys. Rev. A 66:031601
52. Wessel S, Alet F, Troyer M, Batrouni GG. 2004. Phys. Rev. A 70:053615
53. Kato Y, Zhou Q, Kawashima N, Trivedi N. 2008. Nat. Phys. 4:617-21
54. Pollet L, Prokof'ev NV, Svistunov BV. 2010. Phys. Rev. Lett. 104:245705
55. Hirsch JE, Sugar RL, Scalapino DJ, Blankenbecler R. 1982. Phys. Rev. B 26:5033-55
56. Chandrasekharan S, Wiese UJ. 1999. Phys. Rev. Lett. 83:3116-19
57. Suzuki M, Miyashita S, Kuroda A. 1977. Prog. Theor. Phys. 58:1377-87
58. Prokofe'v NV, Svistunov BV, Tupitsyn IS. 1996. JETP Lett. 64:911-16
59. Prokofe'v NV, Svistunov BV, Tupitsyn IS. 1998. Sov. Phys. JETP 87:310-21
60. Handscomb DC. 1962. Proc. Camb. Philos. Soc. 58:594-98
61. Sandvik AW, Singh RRP, Campbell DK. 1997. Phys. Rev. B 56:14510-28
62. Troyer M, Wessel S, Alet F. 2003. Phys. Rev. Lett. 90:12021
63. Sarsa A, Schmidt KE, Magro WR. 2000. J. Chem. Phys. 113:1366-71
64. Vitali E, Rossi M, Tramonto F, Galli DE, Reatto L. 2008. Phys. Rev. B 77:180505
65. Swendsen RH, Wang JS. 1987. Phys. Rev. Lett. 58:86-88
66. Kawashima N, Gubernatis JE. 1994. Phys. Rev. Lett. 73:1295-98
67. Harada K, Kawashima N. 2002. Phys. Rev. E 66:056705
68. Syljuåsen OF, Sandvik AW. 2002. Phys. Rev. E 66:046701
69. Suwa H, Todo S. 2010. Phys. Rev. Lett. 105:120603
70. Rieger H, Kawashima N. 1999. Eur. Phys. J. B 9:233-36
71. Sandvik AW. 2003. Phys. Rev. E 68:056701
72. Liang S, Doucot B, Anderson PW. 1988. Phys. Rev. Lett. 61:365-68
73. Lin YC, Tang Y, Lou J, Sandvik AW. 2012. Phys. Rev. B 86:144405
74. Liang S. 1990. Phys. Rev. B 42:6555-60
75. Santoro G, Sorella S, Guidoni L, Parola A, Tosatti E. 1999. Phys. Rev. Lett. 83:3065-68
76. Sandvik AW. 2005. Phys. Rev. Lett. 95:207203
77. Sutherland B. 1988. Phys. Rev. B 37:3786-89
78. Beach KSD, Sandvik AW. 2006. Nucl. Phys. B 750:142-78
79. Tang Y, Sandvik AW, Henley CL. 2011. Phys. Rev. B 84:174427
80. Affleck I. 1985. Phys. Rev. Lett. 54:966-69
81. Read N, Sachdev S. 1989. Phys. Rev. Lett. 62:1694-97
82. Harada K, Kawashima N, Troyer M. 2003. Phys. Rev. Lett. 90:117203
83. Beach KSD, Alet F, Mambrini M, Capponi S. 2009. Phys. Rev. B 80:184401
84. Kaul RK, Sandvik AW. 2012. Phys. Rev. Lett. 108:137201
85. Plenio MB, Virmani S. 2007. Quant. Inf. Comput. 7:1-51
86. Roscilde T, Verrucchi P, Fubini A, Haas S, Tognetti V. 2005. J. Low Temp. Phys. 140:293-302
87. Fubini A, Roscilde T, Tognetti V, Tusa M, Verrucchi P. 2006. Eur. Phys. J. D 38:563-70
88. Song HF, Rachel S, Flindt C, Klich I, Laflorencie N, Le Hur K. 2012. Phys. Rev. B 85:035409
89. Rachel S, Laflorencie N, Song HF, Le Hur K. 2012. Phys. Rev. Lett. 108:116401
90. Albuquerque AF, Alet F, Sire C, Capponi S. 2010. Phys. Rev. B 81:064418
91. Renyi A. 1961. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4: Contributions to Biology and Problems of Medicine, ed. J Neyman, pp. 547-61. Berkeley: Univ. Calif. Press
92. Holzhey C, Larsen F, Wilczek F. 1994. Nucl. Phys. B 424:443-67
93. Calabrese P, Cardy J. 2004. J. Stat. Mech. 2004:P06002
94. Fradkin E, Moore JE. 2006. Phys. Rev. Lett. 97:050404
95. Buividovich PB, Polikarpov MI. 2008. Nucl. Phys. B 802:458-74
96. Nakagawa Y, Nakamura A, Motoki S, Zakharov VI. 2009. Proc. Sci. LAT2009:188
97. Kallin AB, Hastings MB, Melko RG, Singh RRP. 2011. Phys. Rev. B 84:165134
98. Read N, Sachdev S. 1990. Phys. Rev. B 42:4568-89
99. Murthy G, Sachdev S. 1990. Nucl. Phys. B 344:557-95
100. Motrunich OI, Vishwanath A. 2004. Phys. Rev. B 70:075104
101. Sandvik AW. 2007. Phys. Rev. Lett. 98:227202
102. Sandvik AW, Scalapino DJ. 1994. Phys. Rev. Lett. 72:2777
103. Troyer M, Kontani H, Ueda K. 1996. Phys. Rev. Lett. 76:3822-25
104. Matsumoto M, Yasuda C, Todo S, Takayama H. 2001. Phys. Rev. B 65:014407
105. Wang L, Beach KSD, Sandvik AW. 2006. Phys. Rev. B 73:014431
106. Wenzel S, Bogacz L, Janke W. 2008. Phys. Rev. Lett. 101:127202
107. Wenzel S, Janke W. 2009. Phys. Rev. B 79:014410
108. Jiang FJ. 2012. Phys. Rev. B 85:014414
109. Fritz L, Doretto RL, Wessel S, Wenzel S, Burdin S, Vojta M. 2011. Phys. Rev. B 83:174416
110. Chubukov AV, Sachdev S, Ye J. 1994. Phys. Rev. B 49:11919
111. Sandvik AW, Chubukov AV, Sachdev S. 1995. Phys. Rev. B 51:16483
112. Brenig W. 2006. Phys. Rev. B 73:104450
113. Sandvik AW, Kotov VN, Sushkov OP. 2011. Phys. Rev. Lett. 106:207203
114. Cavadini N, Heigold G, Henggeler W, Furrer A, Güdel HU, et al. 2001. Phys. Rev. B 63:172414
115. Rüegg C, Furrer A, Sheptyakov D, Strässle T, Krämer KW, et al. 2004. Phys. Rev. Lett. 93:257201
116. Rüegg C, Normand B, Matsumoto M, Furrer A, McMorrow DF, et al. 2008. Phys. Rev. Lett. 100:205701
117. Sachdev S. 2009. arXiv:0901.4103. http://qpt.physics.harvard.edu/c49.pdf
118. Troyer M, Zhitomirsky ME, Ueda K. 1997. Phys. Rev. B 55:R6117-20
119. Yasuda C, Todo S, Hukushima K, Alet F, Keller M, et al. 2005. Phys. Rev. Lett. 94:217201
120. Yao DX, Sandvik AW. 2007. Phys. Rev. B 75:052411
121. Jin S, Sandvik AW. 2012. Phys. Rev. B 85:020409
122. Oitmaa J, Kulik Y, Sushkov OP. 2012. Phys. Rev. B 85:144431
123. Chandra P, Doucot B. 1988. Phys. Rev. B 38:9335-38
124. Dagotto E, Moreo A. 1989. Phys. Rev. Lett. 63:2148-51
125. Schulz HJ, Ziman T, Poilblanc D. 1996. J. Phys. I 6:675-703
126. Capriotti L, Becca F, Parola A, Sorella S. 2001. Phys. Rev. Lett. 87:097201
127. Sandvik AW, Daul S, Singh RRP, Scalapino DJ. 2002. Phys. Rev. Lett. 89:247201
128. Sen A, Sandvik AW. 2010. Phys. Rev. B 82:174428
129. Banerjee A, Damle K, Paramekanti A. 2011. Phys. Rev. B 83:134419
130. Rokhsar DS, Kivelson SA. 1988. Phys. Rev. Lett. 61:2376-79
131. Moessner R, Sondhi SL, Fradkin E. 2001. Phys. Rev. B 65:024504
132. Levin M, Senthil T. 2004. Phys. Rev. B 70:220403
133. Jiang FJ, Nyfeler M, Chandrasekharan S, Wiese UJ. 2008. J. Stat. Mech. 2008:P02009
134. Kaul RK, Melko RG. 2008. Phys. Rev. B 78:014417
135. Melko RG, Kaul RK. 2008. Phys. Rev. Lett. 100:017203
136. Lou J, Sandvik AW, Kawashima N. 2009. Phys. Rev. B 80:180414
137. Sandvik AW. 2010. Phys. Rev. Lett. 104:177201
138. Banerjee A, Damle K, Alet F. 2010. Phys. Rev. B 82:155139
139. Giamarchi T, Schulz HJ. 1989. Phys. Rev. B 39:4620-29
140. Nogueira F, Sudbo A. 2012. Phys. Rev. B 86:0451201
141. Sandvik AW. 2012. Phys. Rev. B 85:134407
142. José JV, Kadanoff LP, Kirkpatrick S, Nelson DR. 1977. Phys. Rev. B 16:1217-41
143. Oshikawa M. 2000. Phys. Rev. B 61:3430-34
144. Manuel Carmona J, Pelissetto A, Vicari E. 2000. Phys. Rev. B 61:15136-51
145. Lou J, Sandvik AW, Balents L. 2007. Phys. Rev. Lett. 99:207203
146. Banerjee A, Damle K. 2010. J. Stat. Mech. 2010:P08017
147. Wang L, Sandvik AW. 2010. Phys. Rev. B 81:054417
148. Tang Y, Sandvik AW. 2011. Phys. Rev. Lett. 107:157201
149. Gorshkov AV, Hermele M, Gurarie V, Xu C, Julienne PS, et al. 2010. Nat. Phys. 6:289-95
150. Kugel KI, Khomskii DI. 1982. Sov. Phys. Usp. 25:231-56
151. Barber MN, Batchelor MT. 1989. Phys. Rev. B 40:4621-26
152. Klümper A. 1989. Europhys. Lett. 9:815-20
153. Read N, Sachdev S. 1989. Nucl. Phys. B 316:609-40
154. Sachdev S. 1989. Phys. Rev. B 40:5204-7
155. Syljuåsen OF. 2006. Phys. Rev. B 73:245105
156. Kawashima N, Tanabe Y. 2007. Phys. Rev. Lett. 98:057202
157. Kaul RK. 2011. Phys. Rev. B 84:054407
158. Banerjee A, Damle K, Alet F. 2011. Phys. Rev. B 83:235111
159. Halperin BI, Lubensky TC. 1974. Phys. Rev. Lett. 32:292-95
160. Kaul RK, Sachdev S. 2008. Phys. Rev. B 77:155105
161. Metlitski MA, Hermele M, Senthil T, Fisher MPA. 2008. Phys. Rev. B 78:214418
162. Campostrini M, Hasenbusch M, Pelissetto A, Rossi P, Vicari E. 2002. Phys. Rev. B 65:144520
163. Kuklov AB, Matsumoto M, Prokof'ev NV, Svistunov BV, Troyer M. 2008. Phys. Rev. Lett. 101:050405
164. Kaul RK. 2012. Phys. Rev. B 85:180411
165. Meng ZY, Lang TC, Wessel S, Assaad FF, Muramatsu A. 2010. Nature 464:847-51
166. Jiang HC, Yao H, Balents L. 2012. Phys. Rev. B 86:024424
167. Isakov SV, Kim YB, Paramekanti A. 2006. Phys. Rev. Lett. 97:207204
168. Isakov SV, Paramekanti A, Kim YB. 2007. Phys. Rev. B 76:224431
169. Dang L, Inglis S, Melko RG. 2011. Phys. Rev. B 84:132409
170. Isakov SV, Hastings MB, Melko RG. 2011. Nat. Phys. 7:772-75
171. Banerjee A, Isakov SV, Damle K, Kim YB. 2008. Phys. Rev. Lett. 100:047208
172. Balents L, Fisher MPA, Girvin SM. 2002. Phys. Rev. B 65:224412
173. Misguich G, Lhuillier C. 2005. In Frustrated Spin Systems, ed. HT Diep, pp. 229-96. Singapore: World Sci.
174. Melko RG, Sandvik AW. 2005. Phys. Rev. E. 72:026702
175. Wen XG. 2007. Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons. Oxford, UK: Oxford Univ. Press
176. Hamma A, Ionicioiu R, Zanardi P. 2005. Phys. Lett. A 337:22-28
177. Hamma A, Ionicioiu R, Zanardi P. 2005. Phys. Rev. A 71:022315
178. Levin M, Wen XG. 2006. Phys. Rev. Lett. 96:110405
179. Kitaev A, Preskill J. 2006. Phys. Rev. Lett. 96:110404
180. Flammia ST, Hamma A, Hughes TL, Wen XG. 2009. Phys. Rev. Lett. 103:261601
181. Castelnovo C, Chamon C. 2007. Phys. Rev. B 76:184442
182. Isakov SV, Melko RG, Hastings MB. 2012. Science 335:193-95
183. Chubukov AV, Senthil T, Sachdev S. 1994. Phys. Rev. Lett. 72:2089-92
184. Chubukov AV, Sachdev S, Senthil T. 1994. Nucl. Phys. B 426:601-43
185. Senthil T, Motrunich O. 2002. Phys. Rev. B 66:205104
186. Calabrese P, Pelissetto A, Vicari E. 2002. Phys. Rev. E 65:046115
187. Ballesteros HG, Fernandez LA, Martin-Mayor V, Sudupe AM. 1996. Phys. Lett. B 387:125-31
188. Hasenbusch M, Vicari E. 2011. Phys. Rev. B 84:125136
189. Dorneich A, Troyer M. 2001. Phys. Rev. E 64:066701
190. Bravyi S, DiVincenzo DP, Oliveira RI, Terhal BM. 2008. Quant. Inf. Comp. 8:361-69
191. Sergey Bravyi BMT. 2009. SIAM J. Comput. 39:1462-85
192. White SR, Scalapino DJ, Sugar RL, Loh EY, Gubernatis JE, Scalettar RT. 1989. Phys. Rev. B 40:506-16
193. Assaad FF. 2005. Phys. Rev. B 71:075103
194. Motrunich OI, Fisher MPA. 2007. Phys. Rev. B 75:235116
195. Sorella S, Otsuka Y, Yunoki S. 2012. Sci. Rep. 2:992
196. Troyer M, Wiese UJ. 2005. Phys. Rev. Lett. 94:170201
197. Nakamura T. 1998. Phys. Rev. B 57:R3197-200
198. Chandrasekharan S. 2010. Phys. Rev. D 82:025007
199. Chandrasekharan S, Li A. 2012. Phys. Rev. Lett. 108:140404
200. Corney JF, Drummond PD. 2004. Phys. Rev. Lett. 93:260401
201. Corboz P, Troyer M, Kleine A, McCulloch IP, Schollwöck U, Assaad FF. 2008. Phys. Rev. B 77:085108
202. Nohadani O, Wessel S, Normand B, Haas S. 2004. Phys. Rev. B 69:220402
203. Sengupta P, Batista CD. 2007. Phys. Rev. Lett. 99:217205
204. Harada K, Kawashima N. 2002. Phys. Rev. B 65:052403
205. Harada K, Kawashima N, Troyer M. 2007. J. Phys. Soc. Jpn. 76:013703
206. Wenzel S, Janke W. 2008. Phys. Rev. B 78:064402
207. Hirsch JE. 1985. Phys. Rev. B 31:4403
208. Assaad FF, Imada M, Scalapino DJ. 1996. Phys. Rev. Lett. 77:4592-95
209. Sorella S, Tosatti E. 1992. Europhys. Lett. 19:699
210. Paiva T, Scalettar RT, Zheng W, Singh RRP, Oitmaa J. 2005. Phys. Rev. B 72:085123
211. Clark BK, Abanin DA, Sondhi SL. 2011. Phys. Rev. Lett. 107:087204
212. Lu YM, Ran Y. 2011. Phys. Rev. B 84:024420
213. Wang F. 2010. Phys. Rev. B 82:024419
214. Berg E, Metlitski MA, Sachdev S. 2012. Science 338:1606-9
215. Hv L, Rosch A, Vojta M, Wölfle P. 2007. Rev. Mod. Phys. 79:1015-75
216. Motrunich OI, Senthil T. 2002. Phys. Rev. Lett. 89:277004
217. Vojta T, Schmalian J. 2005. Phys. Rev. Lett. 95:237206
218. Yu R, Roscilde T, Haas S. 2006. Phys. Rev. B 73:064406
219. Roscilde T. 2006. Phys. Rev. B 74:144418
220. Sandvik AW. 2006. Phys. Rev. Lett. 96:207201
221. Roscilde T, Haas S. 2007. Phys. Rev. Lett. 99:047205
222. Yao DX, Gustafsson J, Carlson EW, Sandvik AW. 2010. Phys. Rev. B 82:172409
223. Pollet L, Prokof'ev NV, Svistunov BV, Troyer M. 2009. Phys. Rev. Lett. 103:140402
224. Meier H, Wallin M. 2012. Phys. Rev. Lett. 108:055701
225. Iyer S, Pekker D, Refael G. 2012. Phys. Rev. B 85:094202
226. Gurarie V, Pollet L, Prokof'ev NV, Svistunov BV, Troyer M. 2009. Phys. Rev. B 80:214519
227. Tam KM, Geraedts S, Inglis S, Gingras MJP, Melko RG. 2010. Phys. Rev. Lett. 104:215301
228. Larson D, Kao YJ. 2012. Phys. Rev. Lett. 109:157202
229. Höglund KH, Sandvik AW. 2004. Phys. Rev. B 70:024406
230. Anfuso F, Eggert S. 2006. Phys. Rev. Lett. 96:017204
231. Liu CW, Liu S, Kao YJ, Chernyshev AL, Sandvik AW. 2009. Phys. Rev. Lett. 102:167201
232. Höglund KH, Sandvik AW, Sachdev S. 2007. Phys. Rev. Lett. 98:087203
233. Kaul RK, Melko RG, Metlitski MA, Sachdev S. 2008. Phys. Rev. Lett. 101:187206
234. Sanyal S, Banerjee A, Damle K. 2011. Phys. Rev. B 84:235129
235. Vojta M. 2012. Phys. Rev. B 85:115113
236. Hoyos JA, Vojta T. 2008. Phys. Rev. Lett. 100:240601
237. Vojta T, Kotabage C, Hoyos JA. 2009. Phys. Rev. B 79:024401
238. Altman E, Kafri Y, Polkovnikov A, Refael G. 2010. Phys. Rev. B 81:174528
239. Syljuåsen OF. 2008. Phys. Rev. B 78:174429