Entanglement in SU(2)-invariant quantum spin systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 1, 2003, Pages

  Schliemann, John ^a  

^a UNIVERSITY OF BASEL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETIC MATERIALS; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; STATISTICAL MECHANICS; TENSORS; VECTORS;

CLEBSCH-GORDAN COEFFICIENTS; HILBERT SPACE; ISOTROPIC HEISENBERG SPIN MODEL; PERES-HORODECKI CRITERION; POSITIVE PARTIAL TRANSPOSE; QUANTUM ENTANGLEMENT;

QUANTUM THEORY;

EID: 0141684697     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
2. E. Schrödinger, Naturwissenschaften 23, 807 (1935).
3. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000); for recent reviews on quantum entanglement see Refs. [4-6]
4. M. Lewenstein, D. Bruß, J.I. Cirac, M. Kus, J. Samsonowicz, A. Sanpera, and R. Tarrach, J. Mod. Opt. 47, 2841 (2000).
5. B.M. Terhal, Theor. Comput. Sci. 287, 313 (2002).
6. D. Bruß, J. Math. Phys. 43, 4237 (2002).
7. W.K. Wooters, e-prin quant-ph/0001114.
8. K.M. O'Connor and W.K. Wootters, Phys. Rev. A 63, 052302 (2001).
9. M.C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, 017901 (2001).
10. D. Gunlycke, V.M. Kendon, V. Vedral, and S. Bose, Phys. Rev. A 64, 042302 (2001).
11. X. Wang, H. Fu, and A. I. Solomon, J. Phys. A 34, 11307 (2001).
12. X. Wang, New J. Phys. 4, 11 (2002)
13. X. Wang, Phys. Rev. A 66, 034302 (2002).
14. X. Wang, Phys. Rev. A 66, 044305 (2002).
15. X. Wang and P. Zanardi, Phys. Lett. A 301, 1 (2002).
16. G.L. Kamta and A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002).
17. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) 416, 608 (2002).
18. T.J. Osborne and M.A. Nielsen, Phys. Rev. A 66, 032110 (2002).
19. I. Bose and E. Chattopadhyay, Phys. Rev. A 66, 062320 (2002).
20. D.A. Meyer and N.R. Wallach, J. Math. Phys. 43, 4273 (2002).
21. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).
22. J.I. Latorre, E. Rico, and G. Vidal quant-ph/0304108.
23. B.-Q. Jin and V.E. Korepin, quant-ph/0304108.
24. We note that this restriction to the density matrix excludes spontaneous breaking of the rotational symmetry as it occurs in ferromagnetic of ferrimagnetic phases. However, such symmetry breaking is not possible at finite temperature in systems with a spatial dimension not larger than 2, N.D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966), and systems of this kind are in the focus of previous and present investigations.
25. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
26. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 223, 8 (1996).
27. P. Horodecki, Phys. Lett. A 232, 333 (1997).
28. K.G.H. Vollbrecht and R.F. Werner, Phys. Rev. A 64, 062307 (2002).
29. After submiting an earlier version of this paper, I learned about related unpublished work by B. Hendricks and R.F. Werner [B. Henriks, Diploma thesis, University of Braunschweig, Germany, 2002].
30. * on any operator.
31. C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, and W.K. Wootters, Phys. Rev. A 54, 3824 (1996).
32. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
33. J.M. Radcliffe, J. Phys. A 4, 313 (1971).
34. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer, New York, 1994).
35. H. Bethe, Z. Phys. 71, 205 (1931)
36. L. Hulthén, Ark. Mat., Astron. Fys. 26A, 1 (1938).
37. M. Betsuyaku and T. Yokota, Phys. Rev. B 33, 6505 (1986).
38. M.C. Gutzwiller, Phys. Rev. Lett. 10, 159 (1963).
39. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 59, 121 (1987)
40. F. Gebhard and D. Vollhardt, ibid. 59, 1472 (1987).
41. S. Brehmer, H.-J. Mikeska, and S. Yamamoto, J. Phys.: Condens. Matter 9, 3921 (1997).
42. T. Barnes and E.S. Swanson, Phys. Rev. B 37, 9405 (1988).