Advertisement

Entanglement detachment in fermionic systems

  • Hernán Santos
  • José E. Alvarellos
  • Javier Rodríguez-Laguna
Regular Article
  • 20 Downloads
Part of the following topical collections:
  1. Topical Issue: Quantum Correlations

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.

Graphical abstract

References

  1. 1.
    M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, UK, 2000) Google Scholar
  2. 2.
    L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008) ADSCrossRefGoogle Scholar
  3. 3.
    J. Eisert, M. Cramer, M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010) ADSCrossRefGoogle Scholar
  4. 4.
    M.B. Hastings, J. Stat. Mech. 2007, P08024 (2007) Google Scholar
  5. 5.
    G. Vitagliano, A. Riera, J.I. Latorre, New J. Phys. 12, 113049 (2010) ADSCrossRefGoogle Scholar
  6. 6.
    G. Ramírez, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2014, P10004 (2014) CrossRefGoogle Scholar
  7. 7.
    G. Ramírez, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2015, P06002 (2015) CrossRefGoogle Scholar
  8. 8.
    H. Santos, J.E. Alvarellos, J. Rodríguez-Laguna, https://doi.org/arXiv:1809.06246 (2008)
  9. 9.
    H. Li, F.D.M. Haldane, Phys. Rev. Lett. 101, 010504 (2008) ADSCrossRefGoogle Scholar
  10. 10.
    I. Peschel, J. Phys. A: Math. Gen. 36, L205 (2003) ADSCrossRefGoogle Scholar
  11. 11.
    E. Tonni, J. Rodríguez-Laguna, G. Sierra, J. Stat. Mech. 2018, 043105 (2018) CrossRefGoogle Scholar
  12. 12.
    W. Su, J. Schrieffer, A. Heeger, Phys. Rev. Lett. 42, 1698 (1979) ADSCrossRefGoogle Scholar
  13. 13.
    A.J. Heeger, S. Kivelson, J.R. Schrieffer, W.P. Su, Rev. Mod. Phys. 60, 781 (1988) ADSCrossRefGoogle Scholar
  14. 14.
    J. Sirker, M. Maiti, N.P. Konstantinidis, N. Sedlmayr, J. Stat. Mech.: Theory Exp. 2014, P10032 (2014) CrossRefGoogle Scholar
  15. 15.
    J.K. Asbóth, L. Oroszlány, A. Pályi, A short course on topological insulators (Springer International Publishing, Switzerland, 2016) Google Scholar
  16. 16.
    V. Eisler, I. Peschel, J. Phys. A: Math. Theor. 50, 284003 (2017) CrossRefGoogle Scholar
  17. 17.
    G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) ADSCrossRefGoogle Scholar
  18. 18.
    B.T. Ye, L.Z. Mu, H. Fan, Phys. Rev. B 94, 165167 (2016) ADSCrossRefGoogle Scholar
  19. 19.
    F. Pollmann, A.M. Turner, E. Berg, M. Oshikawa, Phys. Rev. B 81, 064439 (2010) ADSCrossRefGoogle Scholar
  20. 20.
    S. Zilberg, Y. Haas, Int. J. Quantum Chem. 71, 133 (1999) CrossRefGoogle Scholar
  21. 21.
    S. Wiberg, Chem. Rev. 101, 1317 (2001) CrossRefGoogle Scholar
  22. 22.
    S.C.A.H. Pierrefixe, F. Matthias Bickelhaupt, J. Phys. Chem. A 112, 12816 (2008) CrossRefGoogle Scholar
  23. 23.
    R. Breslow, Chem. Record 14, 1174 (2014) CrossRefGoogle Scholar
  24. 24.
    W.J. de Haas, P.M. van Alphen, Proc. Acad. Sci. Amst. 33, 1106 (1930) Google Scholar
  25. 25.
    P.A. Orellana, M.L. Ladrón de Guevara, M. Pacheco, A. Latgé, Phys. Rev. B 68, 195321 (2003) ADSCrossRefGoogle Scholar
  26. 26.
    J.R. Ahn, H.W. Yeom, H.S. Yoon, I.-W. Lyo, Phys. Rev. Lett. 91, 196403 (2003) ADSCrossRefGoogle Scholar
  27. 27.
    J.R. Ahn, P.G. Kang, K.D. Ryang, H.W. Yeom, Phys. Rev. Lett. 95, 196402 (2005) ADSCrossRefGoogle Scholar
  28. 28.
    R. Grüner, Rev. Mod. Phys. 60, 1129 (1988) ADSCrossRefGoogle Scholar
  29. 29.
    M. Lewenstein, A. Sanpera, V. Ahufinger, Ultracold atoms in optical lattices (Oxford University Press, Oxford, UK, 2012) Google Scholar
  30. 30.
    D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005) ADSCrossRefGoogle Scholar
  31. 31.
    O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, New J. Phys. 13, 035002 (2010) CrossRefGoogle Scholar
  32. 32.
    J. Rodríguez-Laguna, L. Tarruell, M. Lewenstein, A. Celi, Phys. Rev. A 95, 013627 (2017) ADSCrossRefGoogle Scholar
  33. 33.
    S. Robles, J. Rodríguez-Laguna, J. Stat. Mech. 2017, 033105 (2017) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dep. de Física Fundamental, Universidad Nacional de Educación a Distancia (UNED)MadridSpain
  2. 2.Dep. de Física de la Materia Condensada, Universidad Autónoma de MadridCantoblancoSpain

Personalised recommendations