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Quantum entanglement in trimer spin-1/2 Heisenberg chains with antiferromagnetic coupling

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Abstract

The quantum entanglement measure is determined, for the first time, for antiferromagnetic trimer spin-1/2 Heisenberg chains. The physical quantity proposed here to measure the entanglement is the distance between states by adopting the Hilbert–Schmidt norm. The method is applied to the new magnetic Cu(II) trimer system, \(\mathrm {2b\cdot 3CuCl_2\cdot 2H_2O}\), and to the trinuclear Cu(II) halide salt, \(\mathrm {(3MAP)_2Cu_2Cl_8}\). The decoherence temperature, above which the entanglement is suppressed, is determined for the both systems. A correlation among their decoherence temperatures and their respective exchange coupling constants is established; moreover, it is conjectured that the exchange coupling protects the system from decoherence as temperature increases.

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Notes

  1. \(b=\mathrm {C_5H_{11}NO_2}\) (betaine). For details concerning crystal structure and magnetic properties, see [11, 12].

  2. 3MAP=3-methyl-2aminopyridinium. For details concerning crystal structure and magnetic properties, see [13].

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  MATH  Google Scholar 

  2. Schrödinger, E.: “Die gegenwärtige Situation in der Quantenmechanik.” Die Naturwissenschaften 23(807), 823–844 (1935)

  3. Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91 (1982)

    Article  Google Scholar 

  4. Nielsen, M.A., Chuang, I.L.: “Quantum computation and quantum information.” Cambridge University Press (2000)

  5. Galindo, A., Martín-Delgado, M.A.: “Information and computation: Classical and quantum aspects.” Rev. Mod. Phys. 74, 347 (2002)

  6. Sachdev, S.: “Quantum phase transitions.” Cambridge University Press (2000)

  7. Somma, R., Ortiz, G., Barnum, H., Knill, E., Viola, L.: Nature and measure of entanglement in quantum phase transitions. Phys. Rev. A 70, 042311 (2004)

    Article  MathSciNet  Google Scholar 

  8. Sarovar, M., Ishizaki, A., Fleming, G.R., Whaley, K.B.: Quantum entanglement in photosynthetic light-harvesting complexes. Nat. Phys. 6, 462 (2010)

    Article  Google Scholar 

  9. Ball, P.: The dawn of quantum biology. Nature 474, 272 (2011)

    Article  Google Scholar 

  10. Sahling, S., Remenyi, G., Paulsen, C., Monceau, P., Saligrama, V., Marin, C., Revcolevschi, A., Regnault, L.P., Raymond, S., Lorenzo, J.E.: Experimental realization of long-distance entanglement between spins in antiferromagnetic quantum spin chains. Nat. Phys. 11, 255 (2015)

    Article  Google Scholar 

  11. Removic-Langer, K., Haussuhl, E., Wiehl, L., Wolf, B., Sauli, F., Hasselmann, n., Kopietz, P., Lang, M.: “Magnetic properties of a novel quasi-\({\rm 2D} {\rm Cu(II)}\) -trimer system.” J. Phys. Cond. Matt. 21, 185013 (2009)

  12. Sanda, M., Kubo, K., Asano, T., Morodomi, H., Inagaki, Y., Kawae, T., Wang, J., Matsuo, A., Kindo, K., Sato, T.J.: Magnetic ordering of antiferromagnetic trimer system \(\rm 2b\cdot 3CuCl_2\cdot 2H_2O\). J. Phys. Conf. Series 400, 032054 (2012)

    Article  Google Scholar 

  13. Grigereit, T.E., Ramakrishna, B.L., Place, H., Willett, R.D., Pellacani, G.C., Manfredini, T., Manabue, L., Bonamartini-Corradi, A., Battaglia, L.P.: Structures and magnetic properties of trinuclear Copper(II) halide salts. Inorg. Chem. 26, 2235 (1987)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Vedral, V., Plenio, M.B.: Entangled measures and purification procedures. Phys. Rev. A 57, 1619 (1998)

    Article  Google Scholar 

  16. Witte, C., Trucks, M.: A new entanglement measure induced by the Hilbert-Schmidt norm. Phys. Lett. A 257, 14 (1999)

    Article  Google Scholar 

  17. Dahl, G., Leinaas, J.M., Myrhein, J., Ovrum, E.: A tensor product matrix approximation problem in quantum physics. Linear Algebra Appl. 420, 711 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. O’Connor, K.M., Wootters, W.K.: Entangled rings. Phys. Rev. A 63, 052302 (2001)

    Article  Google Scholar 

  19. Wang, X., Zanardi, P.: Quantum entanglement and Bell inequalities in Heisenberg spin chains. Phys. Lett. A 301, 1 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bauschke, H.H., Combettes, P. L.: “Convex analysis and monotone operator theory in Hilbert spaces.” Springer, New York (2010)

  22. Wiesniak, M., Vedral, V., Brukner, C.: Magnetic susceptibility as a macroscopic entanglement witness. New J. Phys. 7, 258 (2005)

    Article  Google Scholar 

  23. Tóth, G.: Entanglement detection in optical lattices of bosonic atoms with collective measurements. Phys. Rev. A 69, 052327 (2004)

    Article  Google Scholar 

  24. van Vleck, J.H.: “The theory of electric and magnetic susceptibilities.” Oxford, UK (1932)

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Acknowledgments

The authors thank Afrânio R. Pereira for valuable comments and encouragement, and Géza Tóth for pointed us out the application of the method proposed here to optical lattices. They also thank the referee for useful comments and suggestions. This work was partially supported by the Brazilian agencies, FAPEMIG and CAPES. O.M.D.C. dedicates this work to his father (Oswaldo Del Cima, in memoriam), mother (Victoria M. Del Cima, in memoriam), daughter (Vittoria) and son (Enzo).

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  1. Departamento de Física, Campus Universitário, Universidade Federal de Viçosa (UFV), Avenida Peter Henry Rolfs s/n, Viçosa, MG, 36570-900, Brazil

    O. M. Del Cima, D. H. T. Franco & S. L. L. da Silva

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  1. O. M. Del Cima
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  2. D. H. T. Franco
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  3. S. L. L. da Silva
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Correspondence to O. M. Del Cima.

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Cima, O.M.D., Franco, D.H.T. & da Silva, S.L.L. Quantum entanglement in trimer spin-1/2 Heisenberg chains with antiferromagnetic coupling. Quantum Stud.: Math. Found. 3, 57–63 (2016). https://doi.org/10.1007/s40509-015-0059-1

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