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Aspects of Entanglement in Quantum Many-Body Systems

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Abstract

Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions.

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References

  1. Busch, P., Lahti, P.J., Mittelstaedt, P.: The Quantum Theory of Measurement. Springer, Berlin (1991)

    Google Scholar 

  2. Mittelstaedt, P.: The Interpretation of Quantum Mechanics and the Measurement Process. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  3. Schrödinger, E.: Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  Google Scholar 

  4. Bell, J.S.: Physics 1, 195 (1964)

    Google Scholar 

  5. Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  6. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  7. Vedral, V., Plenio, M.B., Jacobs, K., Knight, P.L.: Phys. Rev. A 56, 4452 (1997)

    Article  ADS  Google Scholar 

  8. Vedral, V., Plenio, B., Rippin, M.A., Knight, P.L.: Phys. Rev. Lett. 78, 2275 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  9. Carteret, H.A., Higuchi, A., Sudbury, A.: J. Math. Phys. 41, 7932 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Dür, W., Vidal, G., Cirac, J.I.: Phys. Rev. A 62, 062314 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  11. Acín, A., Bruß, D., Lewenstein, M., Sanpera, A.: Phys. Rev. Lett. 87, 040401 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  12. Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Rev. Mod. Phys. 80, 517 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  13. Eisert, J., Audenaert, K., Plenio, M.B.: J. Phys. A, Math. Gen. 36, 5605 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Miyake, A.: Phys. Rev. A 67, 012108 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  15. Verstraete, F., Dehaene, J., De Moor, B.: Phys. Rev. A 68, 012103 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  16. Barnum, H., Knill, E., Ortiz, G., Somma, R., Viola, L.: Phys. Rev. Lett. 92, 107902 (2004)

    Article  ADS  Google Scholar 

  17. Somma, R., Ortiz, G., Barnum, H., Knill, E., Viola, L.: Phys. Rev. A 70, 042311 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  18. Mandilara, A., Akulin, V.M., Smilga, A.V., Viola, L.: Phys. Rev. A 74, 002331 (2006)

    Article  ADS  Google Scholar 

  19. Sachdev, S.: Quantum Phase Transitions. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  20. Bucher, E., Ramazashvili, R., Coleman, P.: Nature 407, 351 (2000)

    Article  ADS  Google Scholar 

  21. Coleman, P., Pepin, C., Si, Q., Ramazashvili, R.: J. Phys., Condens. Matter 13, R723 (2001)

    Article  ADS  Google Scholar 

  22. Coleman, P., Pepin, C.: Physica B 312–313, 383 (2002)

    Article  Google Scholar 

  23. Chubukov, A.V., Galitski, V.M., Yakovenko, V.M.: Phys. Rev. Lett. 94, 046404 (2005)

    Article  ADS  Google Scholar 

  24. Gegenwart, P., Si, Q., Steglich, F.: Nat. Phys. 4, 186 (2008)

    Article  Google Scholar 

  25. Khodel, V.A., Clark, J.W., Zverev, M.V.: Phys. Rev. B 78, 075120 (2008)

    Article  ADS  Google Scholar 

  26. Khodel, V.A., Clark, J.W., Zverev, M.V.: JETP Lett. 90, 639 (2009)

    Google Scholar 

  27. Horodecki, M., Horodecki, P., Horodecki, R.: In: Alber, R., Weiner, M. (eds.) Quantum Information: Basic Concepts and Experiments. Springer, Berlin (2001)

    Google Scholar 

  28. Lewenstein, M., et al.: J. Mod. Opt. 47, 2481 (2000)

    MATH  MathSciNet  ADS  Google Scholar 

  29. Acín, A.: Phys. Rev. Lett. 85, 1560 (2000)

    Article  ADS  Google Scholar 

  30. Coester, F.: Nucl. Phys. 7, 421 (1958)

    Article  Google Scholar 

  31. Coester, F., Kümmel, H.: Nucl. Phys. 17, 477 (1960)

    Article  MATH  Google Scholar 

  32. Bishop, R.F.: Theor. Chim. Acta 80, 95 (1991)

    Article  Google Scholar 

  33. Emary, C.: Invited talk presented at the Conference on Microscopic Approaches to Many-Body Theory, University of Manchester, Aug 31–Sept 3, 2005; and private communication

  34. Ristig, M.L., Kim, J.W., Clark, J.W.: In: Clark, J.W., Ristig, M.L. (eds.) Theory of Spin Lattices and Lattice Gauge Models, p. 62. Springer, Berlin (1997)

    Chapter  Google Scholar 

  35. Kim, J.W., Ristig, M.L., Clark, J.W.: Phys. Rev. B 57, 56 (1998)

    Article  ADS  Google Scholar 

  36. Clark, J.W., Ristig, M.L. (eds.): Theory of Spin Lattices and Lattice Gauge Models. Springer, Berlin (1997)

    MATH  Google Scholar 

  37. Clark, J.W., Feenberg, E.: Phys. Rev. 113, 388 (1959)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. Clark, J.W., Westhaus, P.: Phys. Rev. 141, 833 (1966)

    Article  ADS  Google Scholar 

  39. Feenberg, E.: Theory of Quantum Fluids. Academic Press, New York (1969)

    Google Scholar 

  40. Krotscheck, E.: In: Navarro, J., Polls, A. (eds.) Lecture Notes in Physics, vol. 510. Springer, Heidelberg (1998)

    Google Scholar 

  41. Bishop, R.F., Farnell, D.J.J., Ristig, M.L.: Int. J. Mod. Phys. B 14, 1517 (2000)

    ADS  Google Scholar 

  42. Verstraete, F., Popp, M., Cirac, J.I.: Phys. Rev. Lett. 92, 027901 (2004)

    Article  ADS  Google Scholar 

  43. Popp, M., Verstraete, F., Martín-Delagado, M.A., Cirac, J.I.: Phys. Rev. A 71, 042306 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  44. Osborne, T.J., Nielsen, M.A.: Phys. Rev. A 66, 032110 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  45. Osterloh, A., Amico, L., Falci, G., Fazio, R.: Nature 416, 608 (2002)

    Article  ADS  Google Scholar 

  46. Syljuåsen, O.F.: Phys. Lett. A 322, 25 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. Vedral, V.: Cent. Eur. J. Phys. 1, 289 (2003)

    Article  Google Scholar 

  48. Oh, S., Kim, J.: Phys. Rev. A 69, 054305 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  49. Vértesi, T.: Phys. Rev. A 75, 042330 (2007)

    Article  ADS  Google Scholar 

  50. Habibian, H., Clark, J.W., Behbood, N., Hingerl, K.: Phys. Rev. A 81, 032302 (2010)

    Article  ADS  Google Scholar 

  51. Lewenstein, M., Kraus, B., Cirac, J.I., Horodecki, P.: Phys. Rev. A 62, 052310 (2000)

    Article  ADS  Google Scholar 

  52. Gottesman, D.: Phys. Rev. A 54, 1996 (1862)

    MathSciNet  Google Scholar 

  53. Tóth, G., Gühne, O.: Phys. Rev. Lett. 94, 060501 (2005)

    Article  ADS  Google Scholar 

  54. Tóth, G., Gühne, O.: Phys. Rev. A 72, 022340 (2005)

    Article  ADS  Google Scholar 

  55. Jafarizadeh, M.A., Najarbashi, G., Habibian, H.: Phys. Rev. A 75, 052326 (2007)

    Article  ADS  Google Scholar 

  56. Jafarizadeh, M.A., Najarbashi, G., Akbari, Y., Habibian, H.: Eur. Phys. J. D 47, 233 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  57. Clark, J.W.: Prog. Part. Nucl. Phys. 2, 89 (1979)

    Article  ADS  Google Scholar 

  58. Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  59. Wang, X.: Phys. Rev. A 66, 044305 (2002)

    Article  ADS  Google Scholar 

  60. Stelmachovic, P., Buzek, V.: Phys. Rev. A 70, 032313 (2004)

    Article  ADS  Google Scholar 

  61. Lakshminarayan, A., Subrahmanyam, V.: Phys. Rev. A 71, 062334 (2005)

    Article  ADS  Google Scholar 

  62. Bruss, D., Datta, N., Ekert, A., Kwek, L.C., Macchiavello, C.: Phys. Rev. A 72, 014301 (2005)

    Article  ADS  Google Scholar 

  63. Gühne, O., Tóth, G.: Phys. Rev. A 73, 052319 (2006)

    Article  ADS  Google Scholar 

  64. Clark, J.W.: Nucl. Phys. A 328, 587 (1979)

    Article  ADS  Google Scholar 

  65. Feenberg, E.: Ann. Phys. 84, 128 (1974)

    Article  ADS  Google Scholar 

  66. Shi, Y.: J. Phys. A: Math. Gen. 37, 6807 (2004)

    Article  MATH  ADS  Google Scholar 

  67. Lunkes, C., Brukner, C̆., Vedral, V.: Phys. Rev. Lett. 95, 030503 (2005)

    Article  ADS  Google Scholar 

  68. Peres, A.: Phys. Rev. Lett. 77, 1413 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  69. Horodecki, M., Horodecki, P., Horodecki, R.: Phys. Lett. A 223, 1 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Washington University, St. Louis, MO, 63130, USA

    John W. Clark

  2. Grup d’Óptica, Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Spain

    Hessam Habibian

  3. Quantum Information & Communication, École Polytechnique, CP 165, Université Libre de Bruxelles, 1050, Brussels, Belgium

    Aikaterini D. Mandilara

  4. Institut für Theoretische Physik, Universität zu Köln, Cologne, Germany

    Manfred L. Ristig

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  1. John W. Clark
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  2. Hessam Habibian
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  3. Aikaterini D. Mandilara
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  4. Manfred L. Ristig
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Correspondence to John W. Clark.

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Clark, J.W., Habibian, H., Mandilara, A.D. et al. Aspects of Entanglement in Quantum Many-Body Systems. Found Phys 40, 1200–1220 (2010). https://doi.org/10.1007/s10701-010-9467-6

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  • DOI: https://doi.org/10.1007/s10701-010-9467-6

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