Disorder in Quantum Many-Body Systems

Thomas Vojta

doi:10.1146/annurev-conmatphys-031218-013433

Annual Review of Condensed Matter Physics

Volume 10, 2019

Review Article

Free

Disorder in Quantum Many-Body Systems

Thomas Vojta¹
View Affiliations Hide Affiliations

Affiliations: Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA; email: [email protected]
Vol. 10:233-252 (Volume publication date March 2019) https://doi.org/10.1146/annurev-conmatphys-031218-013433
First published as a Review in Advance on December 10, 2018
Copyright © 2019 by Annual Reviews. All rights reserved

Abstract

Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to prevent interesting new quantum states of matter from forming and to smear out sharp features associated with the phase transitions between them. However, disorder is also responsible for a variety of interesting novel phenomena that do not have clean counterparts. These include Anderson localization of single-particle wave functions, many-body localization in isolated many-body systems, exotic quantum critical points, and glassy ground-state phases. This brief review focuses on two separate but related subtopics in this field. First, we review under what conditions different types of randomness affect the stability of symmetry-broken low-temperature phases in quantum many-body systems and the stability of the corresponding phase transitions. Second, we discuss the fate of quantum phase transitions that are destabilized by disorder as well as the unconventional quantum Griffiths phases that emerge in their vicinity.

Keyword(s): disorder, Griffiths phases, Griffiths singularities, quantum phase transitions, randomness, rare regions, symmetry breaking

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031218-013433

2019-03-10

2024-10-04

Full text loading...

/deliver/fulltext/conmatphys/10/1/annurev-conmatphys-031218-013433.html?itemId=/content/journals/10.1146/annurev-conmatphys-031218-013433&mimeType=html&fmt=ahah

Literature Cited

1. Mackenzie A 2017. Disorder in condensed matter physics—experimental perspective. Presented at the Lorentz Cent. Disorder in Condensed Matter and Black Holes Workshop, Leiden
2. Anderson PW 1958. Phys. Rev. 109:1492–505
[Google Scholar]
3. Kramer B, MacKinnon A 1993. Rep. Progr. Phys. 56:1469
[Google Scholar]
4. Evers F, Mirlin AD 2008. Rev. Mod. Phys. 80:1355–417
[Google Scholar]
5. Lee PA, Ramakrishnan TV 1985. Rev. Mod. Phys. 57:287–337
[Google Scholar]
6. Altshuler BL, Aronov AG 1985. Electron-Electron Interactions in Disordered Systems AL Efros, M Pollak1–153 Amsterdam: North Holland:
[Google Scholar]
7. Belitz D, Kirkpatrick TR 1994. Rev. Mod. Phys. 66:261
[Google Scholar]
8. Nandkishore R, Huse DA 2015. Annu. Rev. Condens. Matter Phys. 6:15–38
[Google Scholar]
9. Altman E, Vosk R 2015. Annu. Rev. Condens. Matter Phys. 6:383–409
[Google Scholar]
10. Abanin DA, Papic Z 2017. Ann. Phys. (Leipzig) 529:1700169
[Google Scholar]
11. Ma SK, Dasgupta C, Hu CK 1979. Phys. Rev. Lett. 43:1434
[Google Scholar]
12. Dasgupta C, Ma SK 1980. Phys. Rev. B 22:1305
[Google Scholar]
13. Fisher DS 1994. Phys. Rev. B 50:3799
[Google Scholar]
14. Binder K, Young AP 1986. Rev. Mod. Phys. 58:801–976
[Google Scholar]
15. Fischer KH, Hertz JA 1991. Spin Glasses Cambridge: Cambridge Univ. Press
[Google Scholar]
16. Mydosh J 1993. Spin Glasses: An Experimental Introduction London: Taylor & Francis
[Google Scholar]
17. Vugmeister BE, Glinchuk MD 1990. Rev. Mod. Phys. 62:993–1026
[Google Scholar]
18. Vojta T 2006. J. Phys. A 39:R143
[Google Scholar]
19. Vojta T 2010. J. Low Temp. Phys. 161:299
[Google Scholar]
20. Vojta T, Hoyos JA 2014. Phys. Rev. Lett. 112:075702
[Google Scholar]
21. Landau LD 1937. Zh. Eksp. Teor. Fiz. 7:19
[Google Scholar]
22. Landau LD 1937. Zh. Eksp. Teor. Fiz. 7:627
[Google Scholar]
23. Alet F, Walczak AM, Fisher MPA 2006. Physica A 369:122
[Google Scholar]
24. Castelnovo C, Trebst S, Troyer M 2010. Understanding Quantum Phase Transitions LD Carr169–92 Boca Raton: CRC Press
[Google Scholar]
25. Castelnovo C, Moessner R, Sondhi SL 2012. Annu. Rev. Condens. Matter Phys. 3:35–55
[Google Scholar]
26. Wen XG 2013. ISRN Condens. Matter Phys. 2013:198710
[Google Scholar]
27. Senthil T 2015. Annu. Rev. Condens. Matter Phys. 6:299–324
[Google Scholar]
28. Savary L, Balents L 2017. Rep. Prog. Phys. 80:016502
[Google Scholar]
29. Sachdev S 1999. Quantum Phase Transitions Cambridge: Cambridge Univ. Press
[Google Scholar]
30. Vojta T, Belitz D, Narayanan R, Kirkpatrick TR 1996. Europhys. Lett. 36:191
[Google Scholar]
31. Belitz D, Kirkpatrick TR, Vojta T 2002. Phys. Rev. B 65:165112
[Google Scholar]
32. Belitz D, Kirkpatrick TR, Vojta T 2005. Rev. Mod. Phys. 77:579
[Google Scholar]
33. Vojta T 2013. Lectures On The Physics Of Strongly Correlated Systems XVII A Avella, F Mancini188–247 Melville, NY: AIP
[Google Scholar]
34. Imry Y, Ma Sk 1975. Phys. Rev. Lett. 35:1399–401
[Google Scholar]
35. Aizenman M, Wehr J 1989. Phys. Rev. Lett. 62:2503–6
[Google Scholar]
36. Nattermann T 1983. J. Phys. C 16:6407
[Google Scholar]
37. Greenblatt RL, Aizenman M, Lebowitz JL 2009. Phys. Rev. Lett. 103:197201
[Google Scholar]
38. Aizenman M, Greenblatt RL, Lebowitz JL 2012. J. Math. Phys. 53:023301
[Google Scholar]
39. Kivelson S, Fradkin E, Emery VJ 1998. Nature 393:550–53
[Google Scholar]
40. Fradkin E, Kivelson SA, Lawler MJ, Eisenstein JP, Mackenzie AP 2010. Annu. Rev. Condens. Matter Phys. 1:153–78
[Google Scholar]
41. Fernandes RM, Chubukov AV, Schmalian J 2014. Nat. Phys. 10:97
[Google Scholar]
42. Carlson EW, Dahmen KA, Fradkin E, Kivelson SA 2006. Phys. Rev. Lett. 96:097003
[Google Scholar]
43. Giamarchi T, Le Doussal P 1994. Phys. Rev. Lett. 72:1530–33
[Google Scholar]
44. Gingras MJP, Huse DA 1996. Phys. Rev. B 53:15193–200
[Google Scholar]
45. Fisher DS 1997. Phys. Rev. Lett. 78:1964–67
[Google Scholar]
46. Klein T, Joumard I, Blanchar S, Marcus J, Cubitt R et al. 2001. Nature 413:404
[Google Scholar]
47. Mross DF, Senthil T 2015. Phys. Rev. X 5:031008
[Google Scholar]
48. Bitko D, Rosenbaum TF, Aeppli G 1996. Phys. Rev. Lett. 77:940
[Google Scholar]
49. Tabei SMA, Gingras MJP, Kao YJ, Stasiak P, Fortin JY 2006. Phys. Rev. Lett. 97:237203
[Google Scholar]
50. Silevitch DM, Bitko D, Brooke J, Ghosh S, Aeppli G, Rosenbaum TF 2007. Nature 448:567
[Google Scholar]
51. Schechter M 2008. Phys. Rev. B 77:020401
[Google Scholar]
52. Gingras MJP, Henelius P 2011. J. Phys.: Conf. Ser. 320:012001
[Google Scholar]
53. Kunwar SS, Sen A, Vojta T, Narayanan R 2018. Phys. Rev. B 98:024206
[Google Scholar]
54. Andrade EC, Hoyos JA, Rachel S, Vojta M 2018. Phys. Rev. Lett. 120:097204
[Google Scholar]
55. Schwartz M, Villain J, Shapir Y, Nattermann T 1993. Phys. Rev. B 48:3095–99
[Google Scholar]
56. Hoyos JA, Laflorencie N, Vieira AP, Vojta T 2011. Europhys. Lett. 93:30004
[Google Scholar]
57. Bray AJ, Moore MA 1985. J. Phys. C 18:L927
[Google Scholar]
58. Vojta T 1996. Phys. Rev. B 53:710–14
[Google Scholar]
59. Vojta T, Schreiber M 1996. Phys. Rev. B 53:8211–14
[Google Scholar]
60. Imry Y, Wortis M 1979. Phys. Rev. B 19:3580–85
[Google Scholar]
61. Hui K, Berker AN 1989. Phys. Rev. Lett. 62:2507–10
[Google Scholar]
62. Goswami P, Schwab D, Chakravarty S 2008. Phys. Rev. Lett. 100:015703
[Google Scholar]
63. Senthil T, Majumdar SN 1996. Phys. Rev. Lett. 76:3001
[Google Scholar]
64. Hrahsheh F, Hoyos JA, Vojta T 2012. Phys. Rev. B 86:214204
[Google Scholar]
65. Barghathi H, Hrahsheh F, Hoyos JA, Narayanan R, Vojta T 2015. Phys. Scr. T165:014040
[Google Scholar]
66. Senthil T, Vishwanath A, Balents L, Sachdev S, Fisher MPA 2004. Science 303:1490
[Google Scholar]
67. Senthil T, Balents L, Sachdev S, Vishwanath A, Fisher MPA 2004. Phys. Rev. B 70:144407
[Google Scholar]
68. Harris AB 1974. J. Phys. C 7:1671
[Google Scholar]
69. Weinrib A, Halperin BI 1983. Phys. Rev. B 27:413–27
[Google Scholar]
70. Kinzel W 1985. Z. Phys. B 58:229
[Google Scholar]
71. Alonso JJ, Muñoz MA 2001. Europhys. Lett. 56:485
[Google Scholar]
72. Vojta T, Dickman R 2016. Phys. Rev. E 93:032143
[Google Scholar]
73. Luck JM 1993. Europhys. Lett. 24:359
[Google Scholar]
74. Barghathi H, Vojta T 2014. Phys. Rev. Lett. 113:120602
[Google Scholar]
75. Yao DX, Gustafsson J, Carlson EW, Sandvik AW 2010. Phys. Rev. B 82:172409
[Google Scholar]
76. Ma N, Sandvik AW, Yao DX 2014. Phys. Rev. B 90:104425
[Google Scholar]
77. Chayes JT, Chayes L, Fisher DS, Spencer T 1986. Phys. Rev. Lett. 57:2999
[Google Scholar]
78. Pázmándi F, Scalettar RT, Zimányi GT 1997. Phys. Rev. Lett. 79:5130–33
[Google Scholar]
79. Vojta T 2014. J. Phys. Conf. Ser. 529:012016
[Google Scholar]
80. Motrunich O, Mau SC, Huse DA, Fisher DS 2000. Phys. Rev. B 61:1160
[Google Scholar]
81. Wiseman S, Domany E 1998. Phys. Rev. Lett. 81:22
[Google Scholar]
82. Zhu Q, Wan X, Narayanan R, Hoyos JA, Vojta T 2015. Phys. Rev. B 91:224201
[Google Scholar]
83. Dotsenko VS, Dotsenko VS 1983. Adv. Phys. 32:129–72
[Google Scholar]
84. Shalaev BN 1984. Fiz. Tverd. Tela (Leningrad) 36:3002
[Google Scholar]
85. Shankar R 1987. Phys. Rev. Lett. 58:2466–69
[Google Scholar]
86. Cardy J 1996. J. Phys. A 29:1897
[Google Scholar]
87. Cardy J 1999. Physica A 263:215
[Google Scholar]
88. Fisher DS 1992. Phys. Rev. Lett. 69:534
[Google Scholar]
89. Fisher DS 1995. Phys. Rev. B 51:6411
[Google Scholar]
90. Griffiths RB 1969. Phys. Rev. Lett. 23:17
[Google Scholar]
91. Ibrahim AK, Barghathi H, Vojta T 2014. Phys. Rev. E 90:042132
[Google Scholar]
92. Wortis M 1974. Phys. Rev. B 10:4665
[Google Scholar]
93. Harris AB 1975. Phys. Rev. B 12:203
[Google Scholar]
94. Imry Y 1977. Phys. Rev. B 15:4448
[Google Scholar]
95. Senthil T, Sachdev S 1996. Phys. Rev. Lett. 77:5292
[Google Scholar]
96. Thill M, Huse DA 1995. Physica A 214:321
[Google Scholar]
97. Young AP, Rieger H 1996. Phys. Rev. B 53:8486
[Google Scholar]
98. McCoy BM, Wu TT 1968. Phys. Rev. Lett. 21:549
[Google Scholar]
99. Vojta T 2003. J. Phys. A 36:10921
[Google Scholar]
100. Sknepnek R, Vojta T 2004. Phys. Rev. B 69:174410
[Google Scholar]
101. Millis AJ, Morr DK, Schmalian J 2001. Phys. Rev. Lett. 87:167202
[Google Scholar]
102. Vojta T 2003. Phys. Rev. Lett. 90:107202
[Google Scholar]
103. Hoyos JA, Vojta T 2008. Phys. Rev. Lett. 100:240601
[Google Scholar]
104. Vojta T, Schmalian J 2005. Phys. Rev. B 72:045438
[Google Scholar]
105. Vajk OP, Greven M 2002. Phys. Rev. Lett. 89:177202
[Google Scholar]
106. Sknepnek R, Vojta T, Vojta M 2004. Phys. Rev. Lett. 93:097201
[Google Scholar]
107. Vojta T, Sknepnek R 2006. Phys. Rev. B. 74:094415
[Google Scholar]
108. Prokof'ev N, Svistunov B 2004. Phys. Rev. Lett. 92:015703
[Google Scholar]
109. Iyer S, Pekker D, Refael G 2012. Phys. Rev. B 85:094202
[Google Scholar]
110. Vojta T, Crewse J, Puschmann M, Arovas D, Kiselev Y 2016. Phys. Rev. B 94:134501
[Google Scholar]
111. Mermin ND, Wagner H 1966. Phys. Rev. Lett. 17:1133
[Google Scholar]
112. Vojta T, Igo J, Hoyos JA 2014. Phys. Rev. E 90:012139
[Google Scholar]
113. Brando M, Belitz D, Grosche FM, Kirkpatrick TR 2016. Rev. Mod. Phys. 88:025006
[Google Scholar]
114. Mohan P, Narayanan R, Vojta T 2010. Phys. Rev. B 81:144407
[Google Scholar]
115. Hrahsheh F, Barghathi H, Vojta T 2011. Phys. Rev. B 84:184202
[Google Scholar]
116. Hoyos JA, Kotabage C, Vojta T 2007. Phys. Rev. Lett. 99:230601
[Google Scholar]
117. Vojta T, Kotabage C, Hoyos JA 2009. Phys. Rev. B 79:024401
[Google Scholar]
118. Del Maestro A, Rosenow B, Müller M, Sachdev S 2008. Phys. Rev. Lett. 101:035701
[Google Scholar]
119. Del Maestro A, Rosenow B, Hoyos JA, Vojta T 2010. Phys. Rev. Lett. 105:145702
[Google Scholar]
120. Hooyberghs J, Iglói F, Vanderzande C 2003. Phys. Rev. Lett. 90:100601
[Google Scholar]
121. Vojta T, Dickison M 2005. Phys. Rev. E 72:036126
[Google Scholar]
122. Vojta T, Lee MY 2006. Phys. Rev. Lett. 96:035701
[Google Scholar]
123. Vojta T, Farquhar A, Mast J 2009. Phys. Rev. E 79:011111
[Google Scholar]
124. Vojta T 2012. Phys. Rev. E 86:051137
[Google Scholar]
125. Schehr G, Rieger H 2006. Phys. Rev. Lett. 96:227201
[Google Scholar]
126. Vojta T 2004. Phys. Rev. E 70:026108
[Google Scholar]
127. Dickison M, Vojta T 2005. J. Phys. A 38:1199
[Google Scholar]
128. Dobrosavljevic V, Miranda E 2005. Phys. Rev. Lett. 94:187203
[Google Scholar]
129. Roscilde T, Haas S 2007. Phys. Rev. Lett. 99:047205
[Google Scholar]
130. Weichman PB, Mukhopadhyay R 2008. Phys. Rev. B 77:214516
[Google Scholar]
131. Ubaid-Kassis S, Vojta T, Schroeder A 2010. Phys. Rev. Lett. 104:066402
[Google Scholar]
132. Wang R, Gebretsadik A, Ubaid-Kassis S, Schroeder A, Vojta T et al. 2017. Phys. Rev. Lett. 118:267202
[Google Scholar]
133. Xing Y, Zhang HM, Fu HL, Liu H, Sun Y et al. 2015. Science 350:542–45
[Google Scholar]
134. Mohan P, Goldbart PM, Narayanan R, Toner J, Vojta T 2010. Phys. Rev. Lett. 105:085301
[Google Scholar]
135. Pekker D, Refael G, Demler E 2010. Phys. Rev. Lett. 105:085302
[Google Scholar]
136. Castro Neto AH, Castilla G, Jones BA 1998. Phys. Rev. Lett. 81:3531–34
[Google Scholar]
137. Castro Neto AH, Jones BA 2000. Phys. Rev. B 62:14975
[Google Scholar]
138. Millis AJ, Morr DK, Schmalian J 2002. Phys. Rev. B 66:174433
[Google Scholar]
139. Demkó L, Bordács S, Vojta T, Nozadze D, Hrahsheh F et al. 2012. Phys. Rev. Lett. 108:185701
[Google Scholar]
140. Hrahsheh F, Nozadze D, Vojta T 2011. Phys. Rev. B 83:224402
[Google Scholar]
141. Svoboda C, Nozadze D, Hrahsheh F, Vojta T 2012. Europhys. Lett. 97:20007
[Google Scholar]

/content/journals/10.1146/annurev-conmatphys-031218-013433

Disorder in Quantum Many-Body Systems

Annual Review of Condensed Matter Physics 10, 233 (2019); https://doi.org/10.1146/annurev-conmatphys-031218-013433

/content/journals/10.1146/annurev-conmatphys-031218-013433

Data & Media loading...

Article Type: Review Article

Most Cited Most Cited RSS feed

- Many-Body Localization and Thermalization in Quantum Statistical Mechanics
  
  Rahul Nandkishore, and David A. Huse
  
  Vol. 6 (2015), pp. 15–38
- Search for Majorana Fermions in Superconductors
  
  C.W.J. Beenakker
  
  Vol. 4 (2013), pp. 113–136
- The Mechanics and Statistics of Active Matter
  
  Sriram Ramaswamy
  
  Vol. 1 (2010), pp. 323–345
- Topological Materials: Weyl Semimetals
  
  Binghai Yan, and Claudia Felser
  
  Vol. 8 (2017), pp. 337–354
- Motility-Induced Phase Separation
  
  Michael E. Cates, and Julien Tailleur
  
  Vol. 6 (2015), pp. 219–244
- Correlated Quantum Phenomena in the Strong Spin-Orbit Regime
  
  William Witczak-Krempa, Gang Chen, Yong Baek Kim, and Leon Balents
  
  Vol. 5 (2014), pp. 57–82
- Interface Physics in Complex Oxide Heterostructures
  
  Pavlo Zubko, Stefano Gariglio, Marc Gabay, Philippe Ghosez, and Jean-Marc Triscone
  
  Vol. 2 (2011), pp. 141–165
- Superconducting Qubits: Current State of Play
  
  Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. Wang, Simon Gustavsson, and William D. Oliver
  
  Vol. 11 (2020), pp. 369–395
- Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale
  
  Christopher Jarzynski
  
  Vol. 2 (2011), pp. 329–351
- Strong Correlations from Hund’s Coupling
  
  Antoine Georges, Luca de' Medici, and Jernej Mravlje
  
  Vol. 4 (2013), pp. 137–178
More Less

Annual Review of Condensed Matter Physics

Volume 10, 2019

Review Article

Free

Disorder in Quantum Many-Body Systems

Abstract

Most Read This Month

Most Cited Most Cited RSS feed