Entanglement in valence-bond-solid states on symmetric graphs

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 25, 2010, Pages

  Katsura, Hosho ^a   Kawashima, Naoki ^b   Kirillov, Anatol N ^c   Korepin, Vladimir E ^d   Tanaka, Shu ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TOKYO   (Japan)

^c KYOTO UNIVERSITY   (Japan)

^d STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952992906     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/25/255303     Document Type: Article

References (104)

1. Schrödinger E 1935 Naturwissenschaften 23 807
2. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
3. Lloyd S 1993 Science 261 1569
4. Bennet C H and DiVincenzo D P 2000 Nature 404 247
5. Vidal G, Lattore J I, Rico E and Kitaev A 2003 Phys. Rev. Lett. 90 227902
6. Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 517
7. Kitaev A and Preskill J 2006 Phys. Rev. Lett. 96 110404
8. Levine M and Wen X G 2006 Phys. Rev. Lett. 96 110405
9. Ryu S and Hatsugai Y 2006 Phys. Rev. B 73 245115
10. Ghosh S, Rosenbaum T F, Aeppli G and Coppersmith S N 2003 Nature 425 48
11. Gühne O and Tóth G 2009 Phys. Rep. 474 1
12. Dirac P A M 1930 Proc. Camb. Phil. Soc. 26 376
13. Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
14. Bennet C H, Bernstein H J, Popescu S and Schumacher B 1996 Phys. Rev. A 53 2046
15. Vedral V 2002 Rev. Mod. Phys. 74 197
16. Audenaert K, Eisert J, Plenio M B and Werner R F 2002 Phys. Rev. A 66 042327
17. Cramer M, Eisert J, Plenio M B and Dresig J 2006 Phys. Rev. A 73 012309
18. Jin B Q and Korepin V E 2004 J. Stat. Phys. 116 79
19. Peschel I 2004 J. Stat. Mech. P12005
20. Its A R, Jin B Q and Korepin V E 2005 J. Phys. A: Math. Gen. 38 2975
21. Franchini F, Its A R, Jin B Q and Korepin V E 2007 J. Phys. A: Math. Theor. 40 8467
22. Franchini F, Its A R and Korepin V E 2008 J. Phys. A: Math. Theor. 41 025302
23. Korepin V E and Its A R 2009 J. Stat. Phys. 137 1014
24. Gu S J, Lin H Q and Li Y Q 2004 Phys. Rev. A 68 042330
25. Sato J and Shiroishi M 2007 J. Phys. A: Math. Theor. 40 8739
26. Nienhuis B, Campostrini M and Calabrese P 2009 J. Stat. Mech. P02063
27. Katsura H and Hatsuda Y 2007 J. Phys. A: Math. Theor. 40 13931
28. Korepin V E 2004 Phys. Rev. Lett. 92 096402
29. Calabrese P and Cardy J 2004 J. Stat. Mech. P06002
30. Calabrese P and Cardy J 2009 J. Phys. A: Math. Theor. 42 504005
31. Fan H, Korepin V E and Roychowdhury V 2004 Phys. Rev. Lett. 93 227203
32. Hirano T and Hatsugai Y 2007 J. Phys. Soc. Japan 76 074603
33. Katsura H, Hirano T and Hatsugai Y 2007 Phys. Rev. B 76 012401
34. Hamma A, Ionicioiu R and Zanardi P 2005 Phys. Lett. A 337 22
35. Furukawa S and Misguich G 2007 Phys. Rev. B 75 214407
36. Affleck I, Kennedy T, Lieb E H and Tasaki H 1987 Phys. Rev. Lett. 59 799
37. Affleck I, Kennedy T, Lieb E H and Tasaki H 1988 Commun. Math. Phys. 115 477
38. Verstraete F and Cirac J I 2004 Phys. Rev. A 70 060302
39. Brennen G K and Miyake A 2008 Phys. Rev. Lett. 101 010502
40. Haldane F D M 1983 Phys. Lett. A 93 464
41. Haldane F D M 1983 Phys. Rev. Lett. 50 1153
42. Arovas D P, Auerbach A and Haldane F D M 1988 Phys. Rev. Lett. 60 531
43. den Nijs M and Rommelse K 1989 Phys. Rev. B 40 4709
44. Kennedy T and Tasaki H 1992 Commun. Math. Phys. 147 431
45. Oshikawa M 1992 J. Phys.: Condens. Matter 4 7469
46. Hagiwara M, Katsumata K, Affleck I, Halperin B I and Renard J P 1990 Phys. Rev. Lett. 65 3181
47. Glarum S H, Geschwind S, Lee K M, Kaplan M L and Michel J 1991 Phys. Rev. Lett. 67 1614
48. Kennedy T, Lieb E H and Tasaki H 1988 J. Stat. Phys. 53 383
49. Kirillov A N and Korepin V E 1989 Algebra Anal. 1 47
50. Kirillov A N and Korepin V E 1990 Sankt Petersburg Math. J. 1 47
51. Freitag W D and Müller-Hartmann E 1992 Z. Phys. B 88 279
52. Klümper A, Schadschneider A and Zittarz J 1991 J. Phys. A: Math. Gen. 24 L955
53. Klümper A, Schadschneider A and Zittarz J 1992 Z. Phys. B 87 281
54. Klümper A, Schadschneider A and Zittarz J 1993 Europhys. Lett. 24 293
55. Fannes M, Nachtergaele B and Werner R F 1989 Europhys. Lett. 10 633
56. Fannes M, Nachtergaele B and Werner R F 1991 J. Phys. A: Math. Gen. 24 L185
57. Fannes M, Nachtergaele B and Werner R F 1992 Commun. Math. Phys. 144 443
58. Fannes M, Nachtergaele B and Werner R F 1992 J. Stat. Phys. 66 939
59. Greiter M, Rachel S and Schuricht D 2007 Phys. Rev. B 75 060401
60. Greiter M and Rachel S 2007 Phys. Rev. B 75 184441
61. Rachel S, Thomale R, Fuehringer M, Schmitteckert P and Greiter M 2008 Phys. Rev. B 80 180420
62. Katsura H, Hirano T and Korepin V E 2008 J. Phys. A: Math. Theor. 41 135304
63. Affleck I, Arovas D P, Marston J B and Rabson D A 1991 Nucl. Phys. B 366 467
64. Schuricht D and Rachel S 2008 Phys. Rev. B 78 014430
65. Scalapino D, Zhang S C and Hanke W 1998 Phys. Rev. B 58 443
66. Tu H H, Zhang G M, Xiang T, Liu Z X and Ng T K 2009 Phys. Rev. B 80 014401
67. Tu H H, Zhang G M and Xiang T 2008 J. Phys. A: Math. Theor. 41 415201
68. Arovas D P, Hasebe K, Qi X L and Zhang S C 2009 Phys. Rev. B 79 224404
69. Batchelor M T, Mezincescu L, Nepomechie R I and Rittenberg V 1990 J. Phys. A: Math. Gen. 23 L141
70. Batchelor M T and Yung C M 1994 Int. J. Mod. Phys. B 8 3645
71. Koo W M and Saleur H 1993 Int. J. Mod. Phys. A 8 5165
72. Fannes M, Nachtergaele B and Werner R F 1996 Commun. Math. Phys. 174 477
73. Gils C, Ardonne E, Trebst S, Ludwig A W W, Troyer M and Wang Z 2009 Phys. Rev. Lett. 103 070401
74. Motegi K 2010 arXiv:1003.0050v4 [math-ph]
75. Jozsa R 2005 arXiv:quant-ph/0508124v2
76. Gottesman D and Chuang I 1999 Nature 402 390
77. Nielsen M A 2003 Phys. Lett. A 308 96
78. Leung D W 2004 Int. J. Quantum Inf. 2 33
79. Raussendorf R and Briegel H J 2001 Phys. Rev. Lett. 86 5188
80. Raussendorf R, Browne D E and Briegel H J 2003 Phys. Rev. A 68 022312
81. Briegel H J and Raussendorf R 2001 Phys. Rev. Lett. 86 910
82. Nielsen M A 2006 Rep. Math. Phys. 57 147
83. Gross D and Eisert J 2007 Phys. Rev. Lett. 98 220503
84. Gross D, Eisert J, Schuch N and Perez-Garcia D 2007 Phys. Rev. A 76 052315
85. Yip S K 2003 Phys. Rev. Lett. 90 250402
86. García-Ripoll J J, Martin-Delgado M A and Cirac J I 2004 Phys. Rev. Lett. 93 250405
87. Brennen G K, Micheli A and Zoller P 2007 New J. Phys. 9 138
88. Xu Y, Katsura H, Hirano T and Korepin V E 2008 J. Stat. Phys. 133 347
89. Xu Y, Katsura H, Hirano T and Korepin V E 2008 Quantum Inf. Process. 7 153
90. Korepin V E and Xu Y 2009 arXiv:0908.2345v2 [quant-ph]
91. Verstraete F, Martín-Delgado M A and Cirac J I 2004 Phys. Rev. Lett. 92 087201
92. Orus R 2008 Phys. Rev. A 78 062332
93. Hadley C 2008 Phys. Rev. Lett. 100 170001
94. Fan H, Korepin V E, Roychowdhury V, Hadley C and Bose S 2007 Phys. Rev. B 76 014428
95. Michalakis S and Nachtergaele B 2006 Phys. Rev. Lett. 97 140601
96. Hastings M B 2007 J. Stat. Mech. P08024
97. Niggemann H and Zittarz J 1999 Eur. Phys. J. B 10 731
98. Fan H, Korepin V E and Roychowdhury V 2005 arXiv:quant-ph/0511150v2
99. Eisert J, Cramer M and Plenio M B 2010 Rev. Mod. Phys. 82 277
100. Xu Y and Korepin V E 2008 J. Phys. A: Math. Theor. 41 505302
101. Shi Y, Duan L and Vidal G 2006 Phys. Rev. A 74 022320
102. Niggemann H, Klümper A and Zittarz J 1997 Z. Phys. B 104 103
103. Niggemann H, Klümper A and Zittarz J 2000 Eur. Phys. J. B 13 15
104. Katsura H et al 2010 in preparation