Energy and multipartite entanglement in multidimensional and frustrated spin models

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 5, 2006, Pages

  Gühne, Otfried ^a   Tóth, Géza ^b,c  

^a ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^b MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^c INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON ENERGY LEVELS; LATTICE CONSTANTS; MAGNETIC FIELDS; MATHEMATICAL MODELS;

ENERGY BOUNDS; HEISENBERG MODEL; MACROSCOPIC SPIN MODELS; MULTIPARTITE ENTANGLEMENT;

QUANTUM THEORY;

EID: 33646918556     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.052319     Document Type: Article

References (44)

1. For general results on entanglement in condensed matter systems see A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002);
2. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002);
3. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003);
4. V. E. Korepin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 096402 92, 096402 (2004);
5. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.027901 92, 027901 (2004);
6. H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203 93, 227203 (2004);
7. M. B. Plenio, J. Eisert, J. Dreissig, and M. Cramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060503 94 060503 (2005).
8. For results concerning multipartite entanglement in spin models see X. Wang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.044305 66, 044305 (2002);
9. L. F. Santos, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.062306 67, 062306 (2003);
10. P. Štelmachovič and V. Bužek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.032313 70, 032313 (2004);
11. T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, and V. Tognetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.167203 93, 167203 (2004);
12. T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, and V. Tognetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.147208 94, 147208 (2005);
13. T.-C. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.060305 71, 060305 (R) (2005);
14. D. Bruß, N. Datta, A. Ekert, L. C. Kwek, and C. Macchiavello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.014301 72, 014301 (2005).
15. For a studies on entanglement dynamics in spin systems see, for example, L. Amico, A. Osterloh, F. Plastina, R. Fazio, and G. M. Palma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022304 69, 022304 (2004);
16. M. Koniorczyk, P. Rapcan, and V. Bužek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022321 72, 022321 (2005);
17. A. Sen(De), U. Sen, and M. Lewenstein, e-print quant-ph/0505006.
18. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.040502 93, 040502 (2004);
19. F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227205 93, 227205 (2004);
20. U. Schollwöck, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys. 77.259 77, 259 (2005).
21. G. Tóth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.010301 71, 010301 (R) (2005).
22. Š. Brukner and V. Vedral, e-print quant-ph/0406040.
23. M. R. Dowling, A. C. Doherty, and S. D. Bartlett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062113 70, 062113 (2004).
24. For other works relating the energy to entanglement see A. N. Jordan and M. Büttiker, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 247901 92, 247901 (2004);
25. L.-A. Wu, S. Bandyopadhyay, M. S. Sarandy, and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.032309 72, 032309 (2005).
26. For works relating entanglement to other macroscopic observables, see, e.g., S. Ghosh, T. F. Rosenbaum, G. Aeppli and S. N. Coppersmith, Nature (London) NATUAS 0028-0836 10.1038/nature01888 425, 48 (2003);
27. I. Bose and A. Tribedi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022314 72, 022314 (2005);
28. Š. Brukner, V. Vedral, and A. Zeilinger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012110 73, 012110 (2006);
29. M. Wiesniak, V. Vedral, and Š. Brukner, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/258 7, 258 (2005);
30. T. Vértesi and E. Bene, e-print cond-mat/0503726.
31. O. Gühne, G. Tóth, and H. J. Briegel, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/229 7, 229 (2005).
32. A. Acín, D. Bruß, M. Lewenstein, and A. Sanpera, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.040401 87, 040401 (2001).
33. J. Eisert and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.022306 64, 022306 (2001).
34. C. Lhuillier and G. Misguich, e-print cond-mat/0109146.
35. J. Eisert, P. Hyllus, O. Gühne, and M. Curty, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062317 70, 062317 (2004).
36. L. Hulthén, Ark. Mat., Astron. Fys. AMAFAX 0365-4133 26A, 1 (1938).
37. P. Pfeuty, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(70)90270- 8 57, 79 (1970).
38. D. Porras (private communication).
39. An example for this type of mixed quantum-classical system can be found in G. Tóth and C. S. Lent, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1368389 89, 7943 (2001).
40. S. Katsura, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.127.1508 127, 1508 (1962); erratum: S. Katsura, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.129.2835.4 129, 2835 (1963)
41. For an overview, Frustrated Spin Systems, edited by, H. T. Diep, (World-Scientific, Singapore, 2005);
42. R. Moessner, Can. J. Phys. CJPHAD 0008-4204 10.1139/cjp-79-11-12-1283 79, 1283 (2001).
43. C. M. Dawson and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052316 69, 052316 (2004).
44. See, e.g., J. Richert, e-print cond-mat/0510343.