Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: Different approaches to many-body dynamics far from equilibrium

New Journal of Physics

Volumn 12, Issue , 2010, Pages

  Barmettler, Peter ^a,b   Punk, Matthias ^b   Gritsev, Vladimir ^c   Demler, Eugene ^d   Altman, Ehud ^e  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^d HARVARD UNIVERSITY   (United States)

^e WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CHAINS; NUMERICAL METHODS; OPTICAL LATTICES; QUANTUM OPTICS;

ANALYTICAL APPROACH; ANISOTROPY PARAMETERS; ANTIFERROMAGNETIC ORDERINGS; MANY-BODY DYNAMICS; MANY-BODY SYSTEMS; NON-EQUILIBRIUM DYNAMICS; NUMERICAL MATRICES; OSCILLATORY DYNAMICS;

SPIN DYNAMICS;

EID: 77953046353     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/12/5/055017     Document Type: Article

References (179)

1. Bednorz J G and Müller K A 1986 Z. Phys. B 64 189
2. Feynman R 1986 Found. Phys. 16 507
3. Bloch I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
4. Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
5. Bradley C C, Sackett C A, Tollett J J and Hulet R G 1995 Phys. Rev. Lett. 75 1687
6. Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969
7. Greiner M, Bloch I, Mandel O, Hänsch T W and Esslinger T 2001 Phys. Rev. Lett. 87 160405
8. Greiner M, Bloch I, Hänsch T W and Esslinger T 2001 Phys. Rev. A 63 031401
9. Chin J K, Miller D E, Liu Y, Stan C, Setiawan W, Sanner C, Xu K and Ketterle W 2006 Nature 443 961
10. Zwierlein M W, Schirotzek A, Schunck C H and Ketterle W 2006 Science 311 492
11. Jördens R, Strohmaier N, Gunter K, Moritz H and Esslinger T 2008 Nature 455 204
12. Feshbach H 1958 Ann. Phys. 5 357
13. Tiesinga E, Verhaar B J and Stoof H T C 1993 Phys. Rev. A 47 4114
14. Greiner M, Mandel O, Hänsch T and Bloch I 2002 Nature 419 51
15. Rabl P, Daley A J, Fedichev P O, Cirac J I and Zoller P 2003 Phys. Rev. Lett. 91 110403
16. Kinoshita T, Wenger T and Weiss D S 2006 Nature 440 900
17. Hofferberth S, Lesanovsky I, Fischer B, Schumm T and Schmiedmayer J 2007 Nature 449 324
18. Lee P J, Anderlini M, Brown B L, Sebby-Strabley J, Phillips W D and Porto J V 2007 Phys. Rev. Lett. 99 020402
19. Trotzky S, Cheinet P, Fölling S, Feld M, Schnorrberger U, Rey A M, Polkovnikov A, Demler E A, Lukin M D and Bloch I 2008 Science 319 295
20. Palzer S, Zipkes C, Sias C and Köhi M 2009 Phys. Rev. Lett. 103 150601
21. Trotzky S 2009 private communication
22. Trotzky S, Pollet L, Gerbier F, Schnorrberger U, Bloch I, Prokof'ev N V, Svistunov B and Troyer M 2009 arXiv:0905.4882
23. Damski B 2005 Phys. Rev. Lett. 95 035701
24. Dziarmaga J 2005 Phys. Rev. Lett. 95 245701
25. Cherng R W and Levitov L S 2006 Phys. Rev. A 73 043614
26. Pellegrini F, Montangero S, Santoro G E and Fazio R 2008 Phys. Rev. B 77 140404
27. Polkovnikov A and Gritsev V 2008 Nat. Phys. 4 477
28. Zakrzewski J and Delande D 2009 arXiv:0902.1117
29. Giovannetti V, Lloyd S and Maccone L 2006 Phys. Rev. Lett. 96 010401
30. Mandel O, Greiner M, Widera A, Rom T, Hänsch T W and Bloch I 2003 Nature 425 937
31. Mandel O, Greiner M, Widera A, Rom T, Hänsch T and Bloch I 2003 Phys. Rev. Lett. 91 010407
32. Widera A, Gerbier F, Fölling S, Gericke T, Mandel O and Bloch I 2005 Phys. Rev. Lett. 95 190405
33. Fölling S, Trotzky S, Cheinet P, Feld M, Saers R, Widera A, Muller T and Bloch I 2007 Nature 448 1029
34. Kibble T W B 1976 J. Phys. A: Math. Gen. 9 1387
35. Zurek W H 1985 Nature 317 505
36. Zotos X 1999 Phys. Rev. Lett. 82 1764
37. Kastner M A 1992 Rev. Mod. Phys. 64 849
38. Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A and Zwerger W 1987 Rev. Mod. Phys. 59 1
39. Ogasawara T, Ashida M, Motoyama N, Eisaki H, Uchida S, Tokura Y, Ghosh H, Shukla A, Mazumdar S and Kuwata-Gonokami M 2000 Phys. Rev. Lett. 85 2204
40. Iwai S, Ono M, Maeda A, Matsuzaki H, Kishida H, Okamoto H and Tokura Y 2003 Phys. Rev. Lett. 91 057401
41. Perfetti L, Loukakos P A, Lisowski M, Bovensiepen U, Berger H, Biermann S, Cornaglia P S, Georges A and Wolf M 2006 Phys. Rev. Lett. 97 067402
42. Pfeuty P 1970 Ann. Phys. 57 79
43. Barouch E, McCoy B M and Dresden M 1970 Phys. Rev. A 2 1075
44. Barouch E and McCoy B M 1971 Phys. Rev. A 3 786
45. Barouch E and McCoy B M 1971 Phys. Rev. A 3 2137
46. Shankar R 1994 Rev. Mod. Phys. 66 129
47. Rey A M, Hu B L, Calzetta E, Roura A and Clark C W 2004 Phys. Rev. A 69 033610
48. Gasenzer T, Berges J, Schmidt M G and Seco M 2005 Phys. Rev. A 72 063604
49. Gasenzer T, Berges J, Schmidt M G and Seco M 2007 Nucl. Phys. A 785 214
50. Gasenzer T 2009 Eur. Phys. J. Spl. Top. 168 89
51. Berges J, Borsnyi S and Wetterich C 2004 Phys. Rev. Lett. 93 14202
52. Bettelheim E, Abanov A G and Wiegmann P 2006 Phys. Rev. Lett. 97 246402
53. Cazalilla M A 2006 Phys. Rev. Lett. 97 156403
54. Calabrese P and Cardy J 2006 Phys. Rev. Lett. 96 136801
55. Calabrese P and Cardy J 2007 J. Stat. Mech. P06008
56. Burkov A A, Lukin M D and Demier E 2007 Phys. Rev. Lett. 98 200404
57. Gritsev V, Demler E, Lukin M and Polkovnikov A 2007 Phys. Rev. Lett. 99 200404
58. Iucci A and Cazalilla M 2009 arXiv:0903.1205
59. Sabio J and Kehrein S 2009 arXiv:0911.1302
60. Moeckel M and Kehrein S 2008 Phys. Rev. Lett. 100 175702
61. Hackl A and Kehrein S 2009 J. Phys.: Condens. Matter 21 015601
62. Polkovnikov A, Sachdev S and Girvin S M 2002 Phys. Rev. A 66 053607
63. Polkovnikov A 2003 Phys. Rev. A 68 033609
64. Polkovnikov A 2009 arXiv:0905.3384
65. Jordan P and Wigner E 1928 Z. Phys. 9 631
66. Lieb E, Schultz T and Mattis D 1961 Ann. Phys. 16 407
67. Sengupta K, Powell S and Sachdev S 2004 Phys. Rev. A 69 053616
68. Iglói F and Rieger H 2000 Phys. Rev. Lett. 85 3233
69. Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Phys. Rev. Lett. 98 050405
70. Gangardt D M and Pustilnik M 2008 Phys. Rev. A 77 041604
71. Kollar M and Eckstein M 2008 Phys. Rev. A 78 013626
72. Brioli G, Kollath C and Läuchli A M 2009 arXiv:0907.3731
73. Faribault A, Calabrese P and Caux J S 2009 J. Stat. Mech. P03018
74. Gritsev V, Rostunov T and Demler E 2009 arXiv:0904.3221
75. Rigol M, Dunjko V and Olshanii M 2008 Nature 452 854
76. Läuchli A M and Kollath C 2008 J. Stat. Mech. P05018
77. Roux G 2009 Phys. Rev. A 79 021608
78. Vidal G 2003 Phys. Rev. Lett. 91 147902
79. Daley A J, Kollath C, Schollwöck U and Vidal G 2004 J. Stat. Mech. P04005
80. White S R and Feiguin A E 2004 Phys. Rev. Lett. 93 076401
81. Schollwöck U 2005 Rev. Mod. Phys. 77 259
82. Gobert D, Kollath C, Schollwöck U and Schütz G 2005 Phys. Rev. E 71 036102
83. Chiara G D, Montangero S, Calabrese P and Fazio R 2006 J. Stat. Mech. P03001
84. Manmana S R, Wessel S, Noack R M and Muramatsu A 2007 Phys. Rev. Lett. 98 210405
85. Barmettler P, Rey A M, Demler E, Lukin M D, Bloch I and Gritsev V 2008 Phys. Rev. A 78 012330
86. Barthel T, Kasztelan C, McCulloch I P and Schollwöck U 2009 Phys. Rev. A 79 053627
87. Manmana S R, Wessel S, Noack R M and Muramatsu A 2009 Phys. Rev. B 79 155104
88. Barmettler P, Punk M, Gritsev V,Demler E and Altman E 2009 Phys. Rev. Lett. 102 130603
89. Kollath C, Läuchli A M and Altman E 2007 Phys. Rev. Lett. 98 180601
90. Cramer M, Flesch A, McCulloch IP, Schollwöck U and Eisert J 2008 Phys. Rev. Lett. 101 063001
91. Flesch A, Cramer M, McCulloch I P, Schollwöck U and Eisert J 2008 Phys. Rev. A 78 033608
92. Rigol M 2009 Phys. Rev. Lett. 103 100403
93. Rigol M 2009 Phys. Rev. A 80 053607
94. Freericks J K, Turkowski V M and Zlatić V 2006 Phys. Rev. Lett. 97 266408
95. Eckstein M and Kollar M 2008 Phys. Rev. Lett. 100 120404
96. Eckstein M, Kollar M and Werner P 2009 Phys. Rev. Lett. 103 056403
97. Anderson E et al 1999 LAPACK Users' Guide 3rd edn (Philadelphia, PA: Society for Industrial and Applied Mathematics)
98. Lieb E H and Robinson D W 1972 Commun. Math. Phys. 28 251
99. Calabrese P and Cardy J 2005 J. Stat. Mech.: Theor. Exp. P04010
100. Deutsch J M 1991 Phys. Rev. A 43 2046
101. Belavin A A, Polyakov A M and Zamolodchikov A B 1984 Nucl. Phys. B 241 333
102. Diel H 1997 Int. J. Mod. Phys. B 11 3502
103. Cardy J L 1984 Nucl. Phys. B 240 514
104. Hastings M B and Levitov L S 2008 arXiv:0806.4283
105. Altman E and Auerbach A 2002 Phys. Rev. Lett. 89 250404
106. Barankov R A, Levitov L S and Spivak B Z 2004 Phys. Rev. Lett. 93 160401
107. Antal T, Rácz Z, Rákos A and Schütz G M 1999 Phys. Rev. E 59 4912
108. Giamarchi T 2004 Quantum Physics in One Dimension (Oxford: Oxford University Press)
109. Albuquerque A et al 2007 J. Magn. Magn. Mater. 310 1187
110. Sandvik A W and Kurkijärvi J 1991 Phys. Rev. B 43 5950
111. Alet F, Wessel S and Troyer M 2005 Phys. Rev. E 71 036706
112. Bistritzer R and Altman E 2007 Proc. Natl Acad. Sci. USA 104 9955
113. Ghoshal S and Zamolodchikov A B 1994 Int. J. Mod. Phys. A 9 3841
114. Zamolodchikov A B 1995 Int. J. Mod. Phys. A 10 1125
115. Smirnov F A 1990 Nucl. Phys. B 337 156
116. Lesage F and Saleur H 1997 J. Phys. A: Math. Gen. 30 L457
117. Babujian M K H 2004 Int. J. Mod. Phys. A 192 34
118. Takes G 2008 Nucl. Phys. B 801 187
119. Rossini D, Silva A, Mussardo G and Santoro G E 2009 Phys. Rev. Lett. 102 127204
120. Altshuler B, Konik R and Tsvelik A 2006 Nucl. Phys. B 739 311
121. Sachdev S and Young A P 1997 Phys. Rev. Lett. 78 2220
122. Silva A 2008 Phys. Rev. Lett. 101 120603
123. Polkovnikov A 2008 Phys. Rev. Lett. 101 220402
124. Reimann P 2008 Phys. Rev. Lett. 101 190403
125. Imambekov A and Glazman L I 2009 Science 323 228
126. Smirnov F A 1992 Form Factors in Completely Integrable Models of Quantum Field Theory (Singapore: World Scientific)
127. Controzzi D, Essler F H L and Tsvelik A M 2001 Phys. Rev. Lett. 86 680
128. White S R and Affleck I 2008 Phys. Rev. B 77 134437
129. Barthel T, Schollwöck U and White S R 2009 Phys. Rev. B 79 245101
130. Hastings M B 2009 arXiv:0903.3253
131. Banuls M C, Hastings M B, Verstraete F and Cirac J I 2009 Phys. Rev. Lett. 102 240603
132. Verstraete F, García-Ripoll J J and Cirac J I 2004 Phys. Rev. Lett. 93 207204
133. Jaksch D, Briegel H J, Cirac J I, Gardiner C W and Zoller P 1999 Phys. Rev. Lett. 82 1975
134. Duan L M, Demler E and Lukin M D 2003 Phys. Rev. Lett. 91 090402
135. Anderson P W 1959 Phys. Rev. 115 2
136. Schrieffer J R and Wolff P A 1966 Phys. Rev. 149 491
137. Chao K A, Spalek J and Oles A M 1977 J. Phys. C: Solid State Phys. 10 L271
138. Fazekas P 1999 Lecture Notes on Electron Correlation and Magnetism (Singapore: World Scientific)
139. Bethe H 1931 Z. Phys. 71 205
140. Cloizeaux J D and Gaudin M 1966 J. Math. Phys. 7 1384
141. Yang C N and Yang C P 1966 Phys. Rev. 150 321
142. Yang C N and Yang C P 1966 Phys. Rev. 150 327
143. Yang C N and Yang C P 1966 Phys. Rev. 151 258
144. Baxter R 1973 J. Stat. Phys. 9 145
145. Baxter R 1989 Exactly Solved Problems in Statistical Mechanics (San Diego: Academic)
146. Korepin V E, Bogoliubov N M and Izergin I G 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
147. Kitanine N, Kozlowski K K, Maillet J M, Slavnov N A and Terras V 2009 J. Stat. Mech. P04003
148. Caux J S and Maillet J M 2005 Phys. Rev. Lett. 95 077201
149. Caux J S, Hagemans R and Maillet J M 2005 J. Stat. Mech.: Theor. Exp. P09003
150. Affleck I, Kennedy T, Lieb E H and Tasaki H 1988 Commun. Math. Phys. 115 477
151. Wu T T 1966 Phys. Rev. 149 380
152. McCoy B M and Wu T T 1967 Phys. Rev. 155 438
153. McCoy B M and Wu T T 1967 Phys. Rev. 162 436
154. McCoy B M and Wu T T 1968 Phys. Rev. 174 546
155. Cheng H and Wu T T 1967 Phys. Rev. 164 719
156. Wu T T, McCoy B M, Tracy C A and Barouch E 1976 Phys. Rev. B 13 316
157. Luther A and Peschel I 1975 Phys. Rev. B 12 3908
158. Lukyanov S and Terras V 2003 Nucl. Phys. B 654 323
159. Berezinskii V L 1971 Sov. Phys.- JETP 34 601
160. Kosterlitz J M and Thouless D J 1973 J. Phys. C: Solid State Phys. 6 1181
161. Vidal G 2007 Phys. Rev. Lett. 98 070201
162. Derrida B, Evans M R, Hakim V and Pasquier V 1993 J. Phys. A: Math. Gen. 26 1493
163. Fannes M, Nachtergaele B and Werner R 1992 Commun. Math. Phys. 144 443
164. Klümper A, Schadschneider A and Zittartz J 1991 J. Phys. A: Math. Gen. 24 L955
165. Klümper A, Schadschneider A and Zittartz J 1992 Z. Phys.: Condens. Matter 87 281
166. Anderson P W 1987 Science 235 1196
167. Affleck I, Kennedy T, Lieb E H and Tasaki H 1987 Phys. Rev. Lett. 59 799
168. White S R 1992 Phys. Rev. Lett. 69 2863
169. White S R 1993 Phys. Rev. B 48 10345
170. Östlund S and Rommer S 1995 Phys. Rev. Lett. 75 3537
171. McCulloch IP 2008 arXiv:0804.2509
172. Feiguin A E and White S R 2005 Phys. Rev. B 72 020404
173. Calabrese P and Lefevre A 2008 Phys. Rev. A 78 032329
174. Calabrese P and Cardy J 2004 J. Stat. Mech.: Theor. Exp. P06002
175. Orús R and Vidal G 2008 Phys. Rev. B 78 155117
176. Suzuki M 1990 Phys. Lett. A 146 319
177. McLachlan R I 1995 SIAM J. Sci. Comput. 16 151
178. McCulloch I P 2007 J. Stat. Mech.: Theor. Exp. 2007 P10014
179. García-Ripoll J J 2006 New J. Phys. 8 305