Particle entanglement in continuum many-body systems via quantum Monte Carlo

Physical Review B - Condensed Matter and Materials Physics

Volumn 89, Issue 14, 2014, Pages

  Herdman, C M ^a   Roy, P N ^b   Melko, R G ^b,c   Del Maestro, A ^a  

^a University of Vermont   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

^c PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84899726386     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.89.140501     Document Type: Article

References (63)

1. X. Wen, Int. J. Mod. Phys. B 4, 239 (1990). IJPBEV 0217-9792 10.1142/S0217979290000139
2. C. Nayak, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.1083
3. R. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.865
4. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.517
5. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.666
6. J. Eisert, M. Cramer, and M. B. Plenio, Rev. Mod. Phys. 82, 277 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.277
7. R. G. Melko, A. B. Kallin, and M. B. Hastings, Phys. Rev. B 82, 100409 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.100409
8. H. Ju, A. B. Kallin, P. Fendley, M. B. Hastings, and R. G. Melko, Phys. Rev. B 85, 165121 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.165121
9. S. Humeniuk and T. Roscilde, Phys. Rev. B 86, 235116 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.235116
10. S. Inglis and R. G. Melko, New J. Phys. 15, 073048 (2013). NJOPFM 1367-2630 10.1088/1367-2630/15/7/073048
11. R. R. P. Singh, M. B. Hastings, A. B. Kallin, and R. G. Melko, Phys. Rev. Lett. 106, 135701 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.135701
12. T. Grover, arXiv:1211.1392.
13. J. I. Latorre, J. Phys. A: Math. Theor. 40, 6689 (2007). 1751-8113 10.1088/1751-8113/40/25/S13
14. N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 100, 030504 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.030504
15. See Refs. [30,62,63] for examples of other measures of entanglement of identical particles.
16. P. Zanardi, Phys. Rev. A 65, 042101 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.65.042101
17. Y. Shi, Phys. Rev. A 67, 024301 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.67.024301
18. A. Fang and Y. Chang, Phys. Lett. A 311, 443 (2003). PYLAAG 0375-9601 10.1016/S0375-9601(03)00546-2
19. O. S. Zozulya, M. Haque, and K. Schoutens, Phys. Rev. A 78, 042326 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.042326
20. M. Haque, O. S. Zozulya, and K. Schoutens, J. Phys. A: Math. Theor. 42, 504012 (2009). 1751-8113 10.1088/1751-8113/42/50/504012
21. K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein, Ann. Phys. 299, 88 (2002). APNYA6 0003-4916 10.1006/aphy.2002.6268
22. M. Haque, O. Zozulya, and K. Schoutens, Phys. Rev. Lett. 98, 060401 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.060401
23. O. S. Zozulya, M. Haque, K. Schoutens, and E. H. Rezayi, Phys. Rev. B 76, 125310 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.125310
24. C. Simon, Phys. Rev. A 66, 052323 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.052323
25. V. Vedral, Cent. Eur. J. Phys. 2, 289 (2003). 1895-1082 10.2478/BF02476298
26. W. Ding and K. Yang, Phys. Rev. A 80, 012329 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.80.012329
27. L. Heaney and V. Vedral, Phys. Rev. Lett. 103, 200502 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.200502
28. H. F. Song, S. Rachel, and K. Le Hur, Phys. Rev. B 82, 012405 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.012405
29. The particle entanglement can be nonzero in the absence of interactions for systems of fermions, as well as disconnected systems of bosons, where the entanglement arises from the exchange statistics alone. We focus on contiguous systems of bosons, where the ground state is a BEC.
30. H. M. Wiseman and J. A. Vaccaro, Phys. Rev. Lett. 91, 097902 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.91.097902
31. H. M. Wiseman, S. D. Bartlett, and J. A. Vaccaro, arXiv:quant-ph/0309046.
32. M. R. Dowling, A. C. Doherty, and H. M. Wiseman, Phys. Rev. A 73, 052323 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.73.052323
33. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). RMPHAT 0034-6861 10.1103/RevModPhys.67.279
34. A. Sarsa, K. E. Schmidt, and W. R. Magro, J. Chem. Phys. 113, 1366 (2000). JCPSA6 0021-9606 10.1063/1.481926
35. A. P. Hines, R. H. McKenzie, and G. J. Milburn, Phys. Rev. A 67, 013609 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.67.013609
36. L. Heaney, J. Anders, D. Kaszlikowski, and V. Vedral, Phys. Rev. A 76, 053605 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.76.053605
37. D. Kaszlikowski and M. Wiesniak, arXiv:0712.0990.
38. V. Vedral, arXiv:quant-ph/0703129.
39. J. Goold, L. Heaney, T. Busch, and V. Vedral, Phys. Rev. A 80, 022338 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.80.022338
40. C. N. Gagatsos, A. I. Karanikas, and G. I. Kordas, arXiv:1207.0303.
41. P. Calabrese, M. Mintchev, and E. Vicari, J. Stat. Mech. (2011) P09028.
42. P. Calabrese, M. Mintchev, and E. Vicari, Phys. Rev. Lett. 107, 020601 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.020601
43. K. Burnett, S. Choi, M. Davis, J. A. Dunningham, and S. A. Morgan, C. R. Acad. Sci. Ser. IV Phys. 2, 399 (2001).
44. J. A. Dunningham, S. Bose, L. Henderson, V. Vedral, and K. Burnett, Phys. Rev. A 65, 064302 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.65.064302
45. L. Heaney, arXiv:0711.0942 [quant-ph].
46. O. Penrose and L. Onsager, Phys. Rev. 104, 576 (1956). PHRVAO 0031-899X 10.1103/PhysRev.104.576
47. J. E. Cuervo, P.-N. Roy, and M. Boninsegni, J. Chem. Phys. 122, 114504 (2005). JCPSA6 0021-9606 10.1063/1.1872775
48. M. B. Hastings, I. González, A. B. Kallin, and R. G. Melko, Phys. Rev. Lett. 104, 157201 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.157201
49. J. McMinis and N. M. Tubman, Phys. Rev. B 87, 081108 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.081108
50. For (Equation presented), (Equation presented) is called the SWAP operator in the literature for spatial entanglement. However, we do not use this notation here to avoid confusion with a swap update used in a continuous space worm algorithm.
51. J. Cardy, Phys. Rev. Lett. 106, 150404 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.150404
52. M. Boninsegni and S. Moroni, Phys. Rev. E 86, 056712 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.056712
53. We have chosen to absorb the diagonal weights of the short-time propagator in the estimator into the ensemble weights to improve efficiency [54].
54. C. M. Herdman, S. Inglis, P. N. Roy, R. G. Melko, and A. Del Maestro (unpublished).
55. E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963). PHRVAO 0031-899X 10.1103/PhysRev.130.1605
56. S. Jang, S. Jang, and G. A. Voth, J. Chem. Phys. 115, 7832 (2001). JCPSA6 0021-9606 10.1063/1.1410117
57. The energy gap decreases with (Equation presented) and increases with (Equation presented), so the required (Equation presented) varied from 2 to 12 K(Equation presented).
58. Computing (Equation presented) from numerical integration of (Equation presented) also suffers from a systematic error due to discrete integration; here this systematic error has been reduced to be of the order of the statistical errors.
59. J. Dunningham, A. Rau, and K. Burnett, Science 307, 872 (2005). SCIEAS 0036-8075 10.1126/science.1109545
60. H. Li, R. J. Le Roy, P.-N. Roy, and A. R. W. McKellar, Phys. Rev. Lett. 105, 133401 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.133401
61. F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 104, 190405 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.190405
62. A. P. Balachandran, T. R. Govindarajan, A. R. de Queiroz, and A. F. Reyes-Lega, Phys. Rev. Lett. 110, 080503 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.080503
63. F. Benatti, R. Floreanini, and U. Marzolino, Phys. Rev. A 85, 042329 (2012). PLRAAN 1050-2947 10.1103/PhysRevA.85.042329