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Distribution of entanglement Hamiltonian spectrum in free fermion models

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Abstract

We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the phase of the system: in the delocalized phase it is centered around very small values and in the localized phase, picks of the distribution goes to larger values. We therefore, based on the distribution of entanglement Hamiltonian eigenvalues, explain the behavior of the entanglement entropy in different phases. In addition we propose the smallest magnitude entanglement Hamiltonian eigenvalue as a characterization of phase and phase transition point (although it does not locate the phase transition point very sharply), and we verify it in the mentioned models.

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References

  1. H.-J. Briegel, W. Dür, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 81, 5932 (1998)

    ADS  Google Scholar 

  2. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)

    ADS  MathSciNet  Google Scholar 

  3. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002)

    ADS  Google Scholar 

  4. S.L. Braunstein, H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)

    ADS  Google Scholar 

  5. M.A. Nielsen, I. Chuang, Am. J. Phys. 70, 558 (2002)

    ADS  Google Scholar 

  6. B.E. Kane, Nature 393, 133 EP (1998)

    ADS  Google Scholar 

  7. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    ADS  Google Scholar 

  8. N. Laflorencie, Phys. Rep. 646, 1 (2016)

    ADS  MathSciNet  Google Scholar 

  9. G. Vidal, J. I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)

    ADS  Google Scholar 

  10. P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    ADS  Google Scholar 

  11. K. Le Hur, P. Doucet-Beaupré, W. Hofstetter, Phys. Rev. Lett. 99, 126801 (2007)

    ADS  Google Scholar 

  12. M. Pouranvari, K. Yang, Phys. Rev. B 89, 115104 (2014)

    ADS  Google Scholar 

  13. V. Vedral, M.B. Plenio, M.A. Rippin, P.L. Knight, Phys. Rev. Lett. 78, 2275 (1997)

    ADS  MathSciNet  Google Scholar 

  14. V. Alba, M. Fagotti, P. Calabrese, J. Stat. Mech. 2009, P10020 (2009)

    Google Scholar 

  15. T.-C. Lu, T. Grover, https://arXiv:1808.04381 [cond-mat.stat-mech] (2018)

  16. I. Mondragon-Shem, M. Khan, T.L. Hughes, Phys. Rev. Lett. 110, 046806 (2013)

    ADS  Google Scholar 

  17. S. Vijay, L. Fu, Phys. Rev. B 91, 220101 (2015)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  19. J. Vidal, G. Palacios, R. Mosseri, Phys. Rev. A 69, 022107 (2004)

    ADS  Google Scholar 

  20. L.-A. Wu, M.S. Sarandy, D.A. Lidar, Phys. Rev. Lett. 93, 250404 (2004)

    ADS  MathSciNet  Google Scholar 

  21. B.-B. Wei, Phys. Rev. A 97, 042115 (2018)

    ADS  Google Scholar 

  22. J. Bhattacharya, M. Nozaki, T. Takayanagi, T. Ugajin, Phys. Rev. Lett. 110, 091602 (2013)

    ADS  Google Scholar 

  23. F. Ares, J.G. Esteve, F. Falceto, E. Sánchez-Burillo, J. Phys. A 47, 245301 (2014)

    ADS  MathSciNet  Google Scholar 

  24. P. Caputa, J. Simón, A. Štikonas, T. Takayanagi, J. High Energy Phys. 2015, 102 (2015)

    Google Scholar 

  25. M.J. Gullans, D.A. Huse, https://arXiv:1902.00025 [cond-mat.stat-mech] (2019)

  26. PA. Panda, S. Banerjee, https://arXiv:1904.04270 [cond-mat.dis-nn] (2019)

  27. S.-J. Gu, H.-Q. Lin, Y.-Q. Li, Phys. Rev. A 68, 042330 (2003)

    ADS  Google Scholar 

  28. J. Vidal, R. Mosseri, J. Dukelsky, Phys. Rev. A 69, 054101 (2004)

    ADS  MathSciNet  Google Scholar 

  29. H. Li, F.D.M. Haldane, Phys. Rev. Lett. 101, 010504 (2008)

    ADS  Google Scholar 

  30. F. Pollmann, A.M. Turner, E. Berg, M. Oshikawa, Phys. Rev. B 81, 064439 (2010)

    ADS  Google Scholar 

  31. P. Calabrese, A. Lefevre, Phys. Rev. A 78, 032329 (2008)

    ADS  Google Scholar 

  32. E. Prodan, T.L. Hughes, B.A. Bernevig, Phys. Rev. Lett. 105, 115501 (2010)

    ADS  Google Scholar 

  33. X.-L. Qi, H. Katsura, A.W.W. Ludwig, Phys. Rev. Lett. 108, 196402 (2012)

    ADS  Google Scholar 

  34. H. Yao, X.-L. Qi, Phys. Rev. Lett. 105, 080501 (2010)

    ADS  Google Scholar 

  35. J.I. Cirac, D. Poilblanc, N. Schuch, F. Verstraete, Phys. Rev. B 83, 245134 (2011)

    ADS  Google Scholar 

  36. R. Thomale, D.P. Arovas, B.A. Bernevig, Phys. Rev. Lett. 105, 116805 (2010)

    ADS  Google Scholar 

  37. G. De Chiara, L. Lepori, M. Lewenstein, A. Sanpera, Phys. Rev. Lett. 109, 237208 (2012)

    ADS  Google Scholar 

  38. S. Predin, Europhys. Lett. 119, 57003 (2017)

    ADS  Google Scholar 

  39. G.Y. Cho, A.W.W. Ludwig, S. Ryu, Phys. Rev. B 95, 115122 (2017)

    ADS  Google Scholar 

  40. L. Fidkowski, Phys. Rev. Lett. 104, 130502 (2010)

    ADS  Google Scholar 

  41. M. Pouranvari, K. Yang, Phys. Rev. B 88, 075123 (2013)

    ADS  Google Scholar 

  42. M. Pouranvari, K. Yang, Phys. Rev. B 92, 245134 (2015)

    ADS  Google Scholar 

  43. I. Klich, J. Phys. A 39, L85 (2006)

    ADS  MathSciNet  Google Scholar 

  44. A.D. Mirlin, Y.V. Fyodorov, F.-M. Dittes, J. Quezada, T.H. Seligman, Phys. Rev. E 54, 3221 (1996)

    ADS  Google Scholar 

  45. R.P.A. Lima, H.R. da Cruz, J.C. Cressoni, M.L. Lyra, Phys. Rev. B 69, 165117 (2004)

    ADS  Google Scholar 

  46. K. Slevin, T. Ohtsuki, New J. Phys. 16, 015012 (2014)

    ADS  Google Scholar 

  47. J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010)

    ADS  Google Scholar 

  48. B. Swingle, J. McGreevy Phys. Rev. B 93, 205120 (2016)

    ADS  MathSciNet  Google Scholar 

  49. V. Alba, S.N. Santalla, P. Ruggiero, J. Rodriguez-Laguna, P. Calabrese, G. Sierra, J. Stat. Mech. 2019, 023105 (2019)

    Google Scholar 

  50. S.-A. Cheong, C.L. Henley, Phys. Rev. B 69, 075111 (2004)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

    Mohammad Pouranvari

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  1. Mohammad Pouranvari
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Correspondence to Mohammad Pouranvari.

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Pouranvari, M. Distribution of entanglement Hamiltonian spectrum in free fermion models. Eur. Phys. J. B 93, 118 (2020). https://doi.org/10.1140/epjb/e2020-10052-3

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