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Entanglement detachment in fermionic systems

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Abstract

This article introduces and discusses the concept of entanglement detachment. Under some circumstances, enlarging a few couplings of a Hamiltonian can effectively detach a (possibly disjoint) block within the ground state. This detachment is characterized by a sharp decrease in the entanglement entropy between block and environment, and leads to an increase of the internal correlations between the (possibly distant) sites of the block. We provide some examples of this detachment in free fermionic systems. The first example is an edge-dimerized chain, where the second and penultimate hoppings are increased. In that case, the two extreme sites constitute a block which disentangles from the rest of the chain. Further examples are given by (a) a superlattice which can be detached from a 1D chain, and (b) a star-graph, where the extreme sites can be detached or not depending on the presence of an external magnetic field, in analogy with the Aharonov-Bohm effect. We characterize these detached blocks by their reduced matrices, specially through their entanglement spectrum and entanglement Hamiltonian.

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References

  1. M.A. Nielsen, I.L. Chuang,Quantum computation and quantum information (Cambridge University Press, Cambridge, UK, 2000)

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. M.B. Hastings, J. Stat. Mech. 2007, P08024 (2007)

    Google Scholar 

  5. G. Vitagliano, A. Riera, J.I. Latorre, New J. Phys. 12, 113049 (2010)

    Article  ADS  Google Scholar 

  6. G. Ramírez, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2014, P10004 (2014)

    Article  Google Scholar 

  7. G. Ramírez, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2015, P06002 (2015)

    Article  Google Scholar 

  8. H. Santos, J.E. Alvarellos, J. Rodríguez-Laguna, https://doi.org/arXiv:1809.06246 (2008)

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

    Article  ADS  Google Scholar 

  10. I. Peschel, J. Phys. A: Math. Gen. 36, L205 (2003)

    Article  ADS  Google Scholar 

  11. E. Tonni, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2018, 043105 (2018)

    Article  Google Scholar 

  12. W. Su, J. Schrieffer, A. Heeger, Phys. Rev. Lett. 42, 1698 (1979)

    Article  ADS  Google Scholar 

  13. A.J. Heeger, S. Kivelson, J.R. Schrieffer, W.P. Su, Rev. Mod. Phys. 60, 781 (1988)

    Article  ADS  Google Scholar 

  14. J. Sirker, M. Maiti, N.P. Konstantinidis, N. Sedlmayr, J. Stat. Mech.: Theory Exp. 2014, P10032 (2014)

    Article  Google Scholar 

  15. J.K. Asbóth, L. Oroszlány, A. Pályi,A short course on topological insulators (Springer International Publishing, Switzerland, 2016)

  16. V. Eisler, I. Peschel, J. Phys. A: Math. Theor. 50, 284003 (2017)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. B.T. Ye, L.Z. Mu, H. Fan, Phys. Rev. B 94, 165167 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. S. Zilberg, Y. Haas, Int. J. Quantum Chem. 71, 133 (1999)

    Article  Google Scholar 

  21. S. Wiberg, Chem. Rev. 101, 1317 (2001)

    Article  Google Scholar 

  22. S.C.A.H. Pierrefixe, F. Matthias Bickelhaupt, J. Phys. Chem. A 112, 12816 (2008)

    Article  Google Scholar 

  23. R. Breslow, Chem. Record 14, 1174 (2014)

    Article  Google Scholar 

  24. W.J. de Haas, P.M. van Alphen, Proc. Acad. Sci. Amst. 33, 1106 (1930)

    Google Scholar 

  25. P.A. Orellana, M.L. Ladrón de Guevara, M. Pacheco, A. Latgé, Phys. Rev. B 68, 195321 (2003)

    Article  ADS  Google Scholar 

  26. J.R. Ahn, H.W. Yeom, H.S. Yoon, I.-W. Lyo, Phys. Rev. Lett. 91, 196403 (2003)

    Article  ADS  Google Scholar 

  27. J.R. Ahn, P.G. Kang, K.D. Ryang, H.W. Yeom, Phys. Rev. Lett. 95, 196402 (2005)

    Article  ADS  Google Scholar 

  28. R. Grüner, Rev. Mod. Phys. 60, 1129 (1988)

    Article  ADS  Google Scholar 

  29. M. Lewenstein, A. Sanpera, V. Ahufinger,Ultracold atoms in optical lattices (Oxford University Press, Oxford, UK, 2012)

  30. D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005)

    Article  ADS  Google Scholar 

  31. O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, New J. Phys. 13, 035002 (2010)

    Article  Google Scholar 

  32. J. Rodríguez-Laguna, L. Tarruell, M. Lewenstein, A. Celi, Phys. Rev. A 95, 013627 (2017)

    Article  ADS  Google Scholar 

  33. S. Robles, J. Rodríguez-Laguna, J. Stat. Mech. 2017, 033105 (2017)

    Article  Google Scholar 

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Authors and Affiliations

  1. Dep. de Física Fundamental, Universidad Nacional de Educación a Distancia (UNED), Madrid, Spain

    Hernán Santos, José E. Alvarellos & Javier Rodríguez-Laguna

  2. Dep. de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain

    Hernán Santos

Authors
  1. Hernán Santos
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  2. José E. Alvarellos
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  3. Javier Rodríguez-Laguna
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Corresponding author

Correspondence to Hernán Santos.

Additional information

Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.

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Santos, H., Alvarellos, J.E. & Rodríguez-Laguna, J. Entanglement detachment in fermionic systems. Eur. Phys. J. D 72, 203 (2018). https://doi.org/10.1140/epjd/e2018-90453-7

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