Reduced density matrices and entanglement entropy in free lattice models

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 50, 2009, Pages

  Peschel, Ingo ^a   Eisler, Viktor ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 71049134994     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/50/504003     Document Type: Article

References (109)

1. Dirac P A M 1930 Proc. Camb. Phil. Soc. 26 376
2. Fock V 1931 Z. Phys. 61 126
3. Watanabe S 1939 Z. Phys. 113 482
4. Schrödinger E 1935 Naturwissenschaften 23 807
5. Bombelli L, Koul R K, Lee J and Sorkin R D 1986 Phys. Rev. D 34 373
6. Srednicki M 1993 Phys. Rev. Lett. 71 666
7. Holzhey C, Larsen F and Wilczek F 1994 Nucl. Phys. B 424 443
8. White S R 1992 Phys. Rev. Lett. 69 2863
9. White S R 1993 Phys. Rev. B 48 10345
10. Peschel I, Wang X, Kaulke M and Hallberg K (ed) 1999 Density-Matrix Renormalization (Lecture Notes in Physics vol 528) (Berlin: Springer)
11. Schollwöck U 2005 Rev. Mod. Phys. 77 259
12. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Phys. Rev. Lett. 90 227902
13. Latorre J I, Rico E and Vidal G 2004 Quantum Inf. Comput. 4 48
14. Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 517
15. Peschel I and Eisler V 2008 Computational Many-Particle Physics (Lecture Notes in Physics vol 739) ed H Fehske, R Schneider and A Weisse (Berlin: Springer) pp 581-96
16. Ekert A and Knight P L 1995 Am. J. Phys 63 415
17. Horn R and Johnson C 1991 Topics in Matrix Analysis (Cambridge: Cambridge University Press) chapter 3
18. Schmidt E 1907 Math. Ann. 63 433
19. Li H and Haldane F D M 2008 Phys. Rev. Lett. 101 010504
20. Löwdin P-O 1955 Phys. Rev. 97 1474
21. Plenio M B and Virmani S 2007 Quantum Inf. Comput. 7 1
22. Sato J, Shiroishi M and Takahashi M 2006 J. Stat. Mech. P12017
23. Sato J and Shiroishi M 2007 J. Phys. A: Math. Theor. 40 8739
24. Peschel I and Chung M-C 1999 J. Phys. A: Math. Gen. 32 8419
25. Chung M-C and Peschel I 2000 Phys. Rev. B 62 4191
26. Han D, Kim Y S and Noz M E 1999 Am. J. Phys. 67 61
27. Braunstein S L and van Loock P 2005 Rev. Mod. Phys. 77 513
28. Chung M-C and Peschel I 2001 Phys. Rev. B 64 064412
29. Cheong S A and Henley C L 2004 Phys. Rev. B 69 075111
30. Peschel I 2003 J. Phys. A: Math. Gen. 36 L205
31. Latorre J I and Riera A 2009 J. Phys. A: Math. Theor. 42 504002
32. Lieb E, Schultz T and Mattis D 1961 Ann. Phys. 16 407
33. Audenaert K, Eisert J, Plenio M B and Werner R F 2002 Phys. Rev. A 66 042327
34. Cramer M, Eisert J, Plenio M B and Dreiig J 2006 Phys. Rev. A 73 012309
35. Williamson J 1936 Am. J. Math. 58 141
36. Botero A and Reznik B 2004 Phys. Rev. A 70 052329
37. Adesso G and Illuminati F 2007 J. Phys. A: Math. Theor. 40 7821
38. Casini H and Huerta M 2005 J. Stat. Mech. P12012
39. Barthel T, Chung M-C and Schollwöck U 2006 Phys. Rev. A 74 022329
40. Nishino T and Okunishi K 1997 J. Phys. Soc. Japan 66 3040
41. Peschel I, Kaulke M and Legeza 1999 Ann. Phys. (Leipzig) 8 153
42. Peschel I 2004 J. Stat. Mech. P12005
43. Ercolessi E, Evangelisti S and Ravanini F 2009 arXiv:0905.4000
44. Weston R 2006 J. Stat. Mech. L03002
45. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic)
46. For a brief overview see Cardy J L 1990 Fields, Strings and Critical Phenomena (Les Houches Summer School Session vol 49) ed E Brezin and J Zinn-Justin (Amsterdam: North-Holland) p 169
47. Chung M-C 2002 PhD Thesis Freie Universität Berlin (unpublished)
48. Its A R, Jin B-Q and Korepin V E 2005 J. Phys. A: Math. Gen. 38 2975
49. Legeza and Fth G 1996 Phys. Rev. B 53 14349
50. Okunishi K, Hieida Y and Akutsu Y 1999 Phys. Rev. E 59 R6227
51. Peschel I 2004 J. Stat. Mech. P06004
52. Callan C and Wilczek F 1994 Phys. Lett. B 333 55
53. Truong T T and Peschel I 1988 J. Phys. A: Math. Gen. 21 L1029
54. Davies B 1989 Physica A 159 171
55. Davies B and Pearce P A 1990 J. Phys. A: Math Gen. 23 1295
56. Calabrese P and Lefevre A 2008 Phys. Rev. A 78 032329
57. Calabrese P and Cardy J L 2009 J. Phys. A: Math. Theor. 42 504005
58. Eisler V and Zimbors Z 2005 Phys. Rev. A 71 042318
59. Peschel I 2005 J. Phys. A: Math. Gen. 38 4327
60. du Croo de Jongh M S L 1999 PhD Thesis Leiden University (unpublished)
61. Cramer M, Eisert J and Plenio M B 2007 Phys. Rev. Lett. 98 220603
62. Gaite J 2001 Mod. Phys. Lett. A 16 1109
63. Cheong S A and Henley C L 2004 Phys. Rev. B 69 075112
64. Peschel I and Truong T T 1991 Ann. Phys. 48 185
65. Baxter R J 1977 J. Stat. Phys. 17 1
66. Davies B 1988 Physica A 154 1
67. Truong T T and Peschel I 1989 Z. Phys. B 75 119
68. Nienhuis B, Campostrini M and Calabrese P 2009 J. Stat. Mech. P02063
69. Eisler V, Legeza and Rcz Z 2006 J. Stat. Mech. P11013
70. Iglói F and Juhsz R 2008 Europhys. Lett. 81 57003
71. Calabrese P and Cardy J L 2004 J. Stat. Mech. P06002
72. Franchini F, Its A R, Jin B-Q and Korepin V E 2007 J. Phys. A: Math. Theor. 40 8467
73. Jin B Q and Korepin V E 2004 J. Stat. Phys. 116 79
74. Keating J P and Mezzadri F 2004 Commun. Math. Phys. 252 543
75. Sakai K and Satoh Y 2008 J. High Energy Phys. JHEP12(2008)001
76. Levine G C and Miller D J 2008 Phys. Rev. B 77 205119
77. Iglói F, Szatmri Z and Lin Y-C 2009 Phys. Rev. B 80 024405
78. Eisler V, Iglói F and Peschel I 2009 J. Stat. Mech. P02011
79. Iglói F, Juhsz R and Zimbors Z 2007 Europhys. Lett. 79 37001
80. Laflorencie N 2005 Phys. Rev. B 72 140408
81. Iglói F, Lin Y-C, Rieger H and Monthus C 2007 Phys. Rev. B 76 064421
82. Iglói F and Lin Y-C 2008 J. Stat. Mech. P06004
83. Keating J P, Mezzadri F and Novaes M 2006 Phys. Rev. A 74 012311
84. Eisert J, Cramer M and Plenio M B 2009 Rev. Mod. Phys. (arXiv:0808.3773) at press
85. Wolf M M 2006 Phys. Rev. Lett. 96 010404
86. Gioev D and Klich I 2006 Phys. Rev. Lett. 96 100503
87. Farkas S and Zimbors Z 2007 J. Math. Phys. 48 102110
88. Li W, Ding L, Yu R, Roscilde T and Haas S 2006 Phys. Rev. B 74 073103
89. Eisert J and Cramer M 2005 Phys. Rev. A 72 042112
90. Peschel I and Zhao J 2005 J. Stat. Mech. P11002
91. Orus R, Latorre J I, Eisert J and Cramer M 2006 Phys. Rev. A 73 060303
92. Zhou H Q, Barthel T, Fjærestad J O and Schollwöck U 2006 Phys. Rev. A 74 050305
93. Calabrese P and Cardy J L 2005 J. Stat. Mech. P04010
94. Bloch I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
95. Eisler V and Peschel I 2007 J. Stat. Mech. P06005
96. Bravyi S, Hastings M B and Verstraete F 2006 Phys. Rev. Lett. 97 050401
97. Eisert J and Osborne T J 2006 Phys. Rev. Lett. 97 150404
98. Fagotti M and Calabrese P 2008 Phys. Rev. A 78 010306
99. Rigol M, Muramatsu A and Olshanii M 2006 Phys. Rev. A 74 053616
100. Cramer M, Dawson C M, Eisert J and Osborne T J 2008 Phys. Rev. Lett. 100 030602
101. Barthel T and Schollwöck U 2008 Phys. Rev. Lett. 100 100601
102. Calabrese P and Cardy J L 2007 J. Stat. Mech. P10004
103. Eisler V, Karevski D, Platini T and Peschel I 2008 J. Stat. Mech. P01023
104. Eisler V and Peschel I 2008 Ann. Phys. (Berlin) 17 410
105. Barmettler P, Rey A M, Demler E, Lukin M D, Bloch I and Gritsev V 2008 Phys. Rev. A 78 012330
106. Klich I and Levitov L 2009 Phys. Rev. Lett. 102 100502
107. Harder G 2008 private communication
108. Cherng R W and Levitov L S 2006 Phys. Rev. A 73 043614
109. Cincio L, Dziarmaga J, Rams M M and Zurek W H 2007 Phys. Rev. A 75 052321