Ground state entanglement in quantum spin chains

Quantum Information and Computation

Volumn 4, Issue 1, 2004, Pages 48-92

  Latorre, J I ^a   Rico, E ^a   Vidal, G ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Critical phenomena; Entanglement; Entropy; Spin chain

Indexed keywords

ENTROPY; GROUND STATE; PHASE TRANSITIONS; SPIN DYNAMICS; STATISTICAL MECHANICS;

CONFORMAL FIELD THEORIES; CRITICAL PHENOMENON; DENSITY MATRIX RENORMALIZATION GROUP; ENTANGLEMENT; GROUND-STATE ENTANGLEMENT; QUANTUM PHASE TRANSITIONS; RENORMALIZATION GROUP; SPIN CHAINS;

QUANTUM ENTANGLEMENT;

EID: 1642587733     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (75)

1. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
2. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
3. S. Sachdev, Quantum Phase Transitions, Cambridge Univ. Press (1999).
4. C. H. Bennett and D. P. DiVincenzo, Nature 404, 247 (2000).
5. M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, Cambridge Univ. Press. (2000).
6. Special issue on experimental proposals for quantum computation, Fortschr. Phys. 48, No. 9-11 (2000).
7. J. Preskill, J. Mod. Opt. 47, 127 (2000), quant-ph/9904022.
8. G. Vidal, in preparation.
9. G. Vidal, J. I. Latorre, E. Rico and A. Kitaev, to appear in Phys. Rev. Lett., quant-ph/0211074.
10. M. A. Nielsen, PhD Thesis, University of New Mexico, New Mexico, USA (1998), quant-ph/0011036.
11. W. K. Wootters, quant-ph/0001114.
12. K. M. O'Connor and W. K. Wootters, Phys. Rev. A 63, 052302 (2001), quant-ph/0009041.
13. M. C. Arnesen, S. Bose and V. Vedral, Phys. Rev. Lett. 87, 017901 (2001), quant-ph/0009060.
14. D. Gunlycke, S. Bose, V.M. Kendon, V. Vedral, Phys. Rev. A 64, 042302 (2001), quant-ph/0102137.
15. X. Wang, H. Fu and A. I. Solomon, J. Phys. A: Math. Gen. 34 (50), 11307-11320 (2001), quant-ph/0105075.
16. X. Wang and P. Zanardi, Phys. Lett. A 301 (1-2), 1 (2002), quant-ph/0202108.
17. X. Wang, Phys. Rev. A 66, 034302 (2002), quant-ph/0203141.
18. P. Zanardi and X. Wang, J. Phys. A 35, 7947 (2002), quant-ph/0201028; Yu Shi, quant-ph/0204058 and cond-mat/0205272; K. Audenaert, J. Eisert, M.B. Plenio and R.F. Werner, Phys. Rev. A 66, 042327 (2002), quant-ph/0205025; M. A. Martín-Delgado, quant-ph/0207026; J. Schliemann, quant-ph/0212114.
19. P. Zanardi and X. Wang, J. Phys. A 35, 7947 (2002), quant-ph/0201028; Yu Shi, quant-ph/0204058 and cond-mat/0205272; K. Audenaert, J. Eisert, M.B. Plenio and R.F. Werner, Phys. Rev. A 66, 042327 (2002), quant-ph/0205025; M. A. Martín-Delgado, quant-ph/0207026; J. Schliemann, quant-ph/0212114.
20. P. Zanardi and X. Wang, J. Phys. A 35, 7947 (2002), quant-ph/0201028; Yu Shi, quant-ph/0204058 and cond-mat/0205272; K. Audenaert, J. Eisert, M.B. Plenio and R.F. Werner, Phys. Rev. A 66, 042327 (2002), quant-ph/0205025; M. A. Martín-Delgado, quant-ph/0207026; J. Schliemann, quant-ph/0212114.
21. P. Zanardi and X. Wang, J. Phys. A 35, 7947 (2002), quant-ph/0201028; Yu Shi, quant-ph/0204058 and cond-mat/0205272; K. Audenaert, J. Eisert, M.B. Plenio and R.F. Werner, Phys. Rev. A 66, 042327 (2002), quant-ph/0205025; M. A. Martín-Delgado, quant-ph/0207026; J. Schliemann, quant-ph/0212114.
22. P. Zanardi and X. Wang, J. Phys. A 35, 7947 (2002), quant-ph/0201028; Yu Shi, quant-ph/0204058 and cond-mat/0205272; K. Audenaert, J. Eisert, M.B. Plenio and R.F. Werner, Phys. Rev. A 66, 042327 (2002), quant-ph/0205025; M. A. Martín-Delgado, quant-ph/0207026; J. Schliemann, quant-ph/0212114.
23. A. Osterloh, L. Amico, G. Falci and R. Fazio, Nature 416, 608 (2002), quant-ph/0202029.
24. T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002), quant-ph/0202162.
25. E. Lieb, T. Schultz and D. Mattis, Annals of Phys. 16 407 (1961).
26. S. Katsura, Phys. Rev. 127 1508 (1962)
27. E. Barouch and B. McCoy, Phys. Rev. A 3 786 (1971)
28. H. Bethe, Z. Phys. 71, 205 (1931).
29. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993), hep-th/9303048.
30. C. G. Callan and F. Wilczek, Phys. Lett.B 333 (1994) 55, hep-th/9401072.
31. T. M. Fiola, J. Preskill, A. Strominger and S. P. Trivedi, Phys. Rev. D 50 (1994) 3987, hep-th/9403137.
32. C. Holzhey, F. Larsen and F. Wilczek, Nucl.Phys.B 424 (1994) 443, hep-th/9403108.
33. S. R. White, Phys. Rev. B 48, 10345 (1993).
34. S. Rommer and S. Östlund, "Density matrix renormalization", Dresden, 1998 (Springer, Berlin, 1999), pp 67-89.
35. A. B. Zamolodchikov, JETP Lett. 43 (1986) 730.
36. C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher, Phys. Rev. A 53, 2046 (1996), quant-ph/9511030.
37. Quan. Inf. Comp. 1 (2001).
38. M. A. Nielsen, Phys. Rev. Lett. 83, 436 (1999); quant-ph/9811053.
39. G. Vidal, J. Mod. Opt. 47, 355 (2000), quant-ph/9807077. G. Vidal, Phys. Rev. Lett. 83, 1046 (1999).
40. G. Vidal, J. Mod. Opt. 47, 355 (2000), quant-ph/9807077. G. Vidal, Phys. Rev. Lett. 83, 1046 (1999).
41. W. Dür, G. Vidal, J. I. Cirac, Phys. Rev. A 62, 062314 (2000), quant-ph/0005115.
42. G. Vidal, quant-ph/0301063.
43. W. K.Wootters, Phys. Rev. Lett. 80, 2245 (1998), quant-ph/9709029.
44. V. Coffman, J. Kundu, W. K. Wootters, Phys. Rev. A 61 052306 (2000), quant-ph/9907047.
45. M. Ohya and D. Petz, Quantum entropy and its use (Springer-Verlag Berlin, 1993).
46. E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14 1938 (1973)
47. P. Stelmachovic and V. Buzek, presented at a quantum information conference in Gdansk (July 2001) and in San Feliu (March 2002).
48. R. Bhatia, Matrix Analisis, Graduate Texts in Mathematics vol. 169, Springer-Verlag (1996).
49. M. A. Nielsen and G. Vidal, Quant. Inf. and Comp. 1, 76 (2001).
50. T. J. Osborne and M. A. Nielsen, Quant. Inf. Proc. 1, 45 (2002), quant-ph/0109024.
51. I. Peschel, M. Kaulke and O. Legeza, Ann. Physik (Leipzig) 8 (1999) 153, cond-mat/9810174; M. C. Chung and I. Peschel Phys. Rev. B 64 064412 (2001), cond-mat/0103301; I. Peschel, J. Phys. A: Math. Gen. 36 L205 (2003), cond-mat/0212631.
52. I. Peschel, M. Kaulke and O. Legeza, Ann. Physik (Leipzig) 8 (1999) 153, cond-mat/9810174; M. C. Chung and I. Peschel Phys. Rev. B 64 064412 (2001), cond-mat/0103301; I. Peschel, J. Phys. A: Math. Gen. 36 L205 (2003), cond-mat/0212631.
53. I. Peschel, M. Kaulke and O. Legeza, Ann. Physik (Leipzig) 8 (1999) 153, cond-mat/9810174; M. C. Chung and I. Peschel Phys. Rev. B 64 064412 (2001), cond-mat/0103301; I. Peschel, J. Phys. A: Math. Gen. 36 L205 (2003), cond-mat/0212631.
54. P. Christe and M. Henkel, Introduction to conformal invariance and its applications to critical phenomena, Ed. Springer-Verlag m.16.
55. B. K. Chakrabarti, A. Dutta and P. Sen, Quantum Ising phases and Transitions in Transverse Ising Models, Ed. Spinger m.41.
56. A. Kitaev, cond-mat/0010440.
57. R. Orbach, Phys. Rev. 112, 309 (1958).
58. C. N. Yang and C. P. Yang, Phys. Rev. 150, 321 (1966).
59. J. C. Bonner and M. E. Fisher, Phys. Rev. 135, A640 (1964).
60. I. Affleck., J. Phys. A 31, 4573 (1998), cond-mat/9802045.
61. J. D. Bekenstein gr-qc/9409015.
62. Paul Ginsparg, Applied conformal field theory Les Houches Summer School 1988, pp 1-168.
63. D. Kabat and M. J. Strassler, Phys. Lett. B 329, 46 (1994), hep-th/9401125; D. Kabat, Nucl. Phys. B453, 281 (1995), hep-th/9503016.
64. D. Kabat and M. J. Strassler, Phys. Lett. B 329, 46 (1994), hep-th/9401125; D. Kabat, Nucl. Phys. B453, 281 (1995), hep-th/9503016.
65. N. D. Birrel and P. C. W. Davies, Quantum fields in curved space, Cambridge University Press (1982).
66. J. Gaite, Mod. Phys. Lett. A16, 1109 (2001), cond-mat/0106049.
67. T. R. Morris, Phys. Lett. B 329, 241 (1994), hep-th/9403340; J. Berges, N. Tetradis and C. Wetterich, Phys. Rept. 363, 223 (2002), hep-ph/0005122; R. D. Ball et al. Phys. Lett. B 347, 80 (1995), hep-th/9411122.
68. T. R. Morris, Phys. Lett. B 329, 241 (1994), hep-th/9403340; J. Berges, N. Tetradis and C. Wetterich, Phys. Rept. 363, 223 (2002), hep-ph/0005122; R. D. Ball et al. Phys. Lett. B 347, 80 (1995), hep-th/9411122.
69. T. R. Morris, Phys. Lett. B 329, 241 (1994), hep-th/9403340; J. Berges, N. Tetradis and C. Wetterich, Phys. Rept. 363, 223 (2002), hep-ph/0005122; R. D. Ball et al. Phys. Lett. B 347, 80 (1995), hep-th/9411122.
70. J. L. Cardy, Phys. Lett. B 215, 749 (1988).
71. A. Cappelli, D. Friedan and J.I. Latorre, Nucl. Phys. B 352 (1991) 616.
72. A. Cappelli, J. I. Latorre and X. Vilasís-Cardona, Nucl. Phys. B 376, 510 (1992), hep-th/9109041.
73. H. Osborn and G.M. Shore, Nucl. Phys. B 571, 287 (2000), hep-th/9909043.
74. D. Anselmi, Nucl. Phys. B 567, 331 (2000), hep-th/9905005.
75. S. Forte and J. I. Latorre, Nucl. Phys. B 535 (1998) 709, hep-th/9805015.