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An Ab Initio Evaluation of Mott Properties?

  • A. Cabo Montes de Oca
Chapter

Abstract

A GW scheme for band calculations is proposed. It rests on the static approximation for the effective potential. A closed system of equations for the determination of the basis of filled and empty states is obtained. The full translational symmetry in the original lattice is allowed to be broken and the wavefunction basis admits non-collinear spin dependences. The results of its planned application to the La\(_2\)CuO\(_4\) crystal are expected to reproduce the strong correlation properties which emerged from a previously studied closely related model. A positive result of this study could show an example of the derivation of the Mott properties of a model without the need of introducing auxiliary phenomenological conditions. Thus, a path for derive the properties of strongly correlated electron systems (SCES) from ab initio calculations is suggested.

Notes

Acknowledgements

It is for me a real pleasure to participate in this tribute in honor of dear Professor N. H. March, who so much had contributed not only to theoretical condensed matter physics but also to support the formation of Third World physicists. In particular I always remember those visits to the International Center for Theoretical Physics (ICTP, Trieste, Italy) during the eighties, in which the participants coming from developing countries were almost ‘forced’ to communicate and collaborate among them within seminars and discussion meetings organized by Professors March, Butcher, Garcia-Moliner, etc. In my case, I clearly remember a final meeting with Professors March and Butcher at the end of the first of those visits, in which my motivation was to start applying quantum field theory (QFT) methods in condensed matter problems. In that encounter, they recommended me to consider the investigation of the physics of inhomogeneous electron systems, a line of work that I followed up to nowadays. In particular, this work is closely connected with that initial recommendation.

References

  1. 1.
    N.F. Mott, Proc. Phys. Soc. A 62(7), 416 (1949).  https://doi.org/10.1088/0370-1298/62/7/303
  2. 2.
    J.C. Slater, Phys. Rev. 81, 385 (1951).  https://doi.org/10.1103/PhysRev.81.385
  3. 3.
    J.C. Slater, Quantum Theory of Atomic Structure, vol. 2 (Dover, New York, 1960)Google Scholar
  4. 4.
    J.G. Bednorz, K.A. Müller, Rev. Mod. Phys. 60, 585 (1988).  https://doi.org/10.1103/RevModPhys.60.585
  5. 5.
    E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).  https://doi.org/10.1103/RevModPhys.66.763
  6. 6.
    C. Almasan, M.B. Maple, Chemistry of High Temperature Superconductors (World Scientific, Singapore, 1991)Google Scholar
  7. 7.
    Y. Yanase, T. Jujo, T. Nomura, H. Ikeda, T. Hotta, K. Yamada, Phys. Rep. 387(1–4), 1 (2003).  https://doi.org/10.1016/j.physrep.2003.07.002
  8. 8.
    D.J. Van Harlingen, Rev. Mod. Phys. 67, 515 (1995).  https://doi.org/10.1103/RevModPhys.67.515
  9. 9.
    A. Damascelli, Z. Hussain, Z.X. Shen, Rev. Mod. Phys. 75, 473 (2003).  https://doi.org/10.1103/RevModPhys.75.473
  10. 10.
    W.E. Pickett, Rev. Mod. Phys. 61, 433 (1989).  https://doi.org/10.1103/RevModPhys.61.433
  11. 11.
    G. Burns, High Temperature Superconductivity: An Introduction (Academic Press, New York, 1992)Google Scholar
  12. 12.
    M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).  https://doi.org/10.1103/RevModPhys.70.1039
  13. 13.
    T. Freltoft, J.P. Remeika, D.E. Moncton, A.S. Cooper, J.E. Fischer, D. Harshman, G. Shirane, S.K. Sinha, D. Vaknin, Phys. Rev. B 36, 826 (1987).  https://doi.org/10.1103/PhysRevB.36.826
  14. 14.
    J.H. de Boer, E.J.W. Verwey, Proc. Phys. Soc. 49(4S), 59 (1937).  https://doi.org/10.1088/0959-5309/49/4S/307
  15. 15.
    N.F. Mott, R. Peierls, Proc. Phys. Soc. 49(4S), 72 (1937).  https://doi.org/10.1088/0959-5309/49/4S/308
  16. 16.
    P.W. Anderson, Phys. Rev. 115, 2 (1959).  https://doi.org/10.1103/PhysRev.115.2
  17. 17.
    J. Hubbard, Proc. R. Soc. Lond. A 276(1365), 238 (1963).  https://doi.org/10.1098/rspa.1963.0204
  18. 18.
    P.W. Anderson, Science 235, 1196 (1987).  https://doi.org/10.1126/science.235.4793.1196
  19. 19.
    E. Fradkin, Field Theories of Condensed Matter Systems (Addison-Wesley, Redwood City, 1991)Google Scholar
  20. 20.
    M.C. Gutzwiller, Phys. Rev. 134, A923 (1964).  https://doi.org/10.1103/PhysRev.134.A923
  21. 21.
    M.C. Gutzwiller, Phys. Rev. 137, A1726 (1965).  https://doi.org/10.1103/PhysRev.137.A1726
  22. 22.
    W.F. Brinkman, T.M. Rice, Phys. Rev. B 2(10), 4302 (1970).  https://doi.org/10.1103/PhysRevB.2.4302
  23. 23.
    W. Kohn, Phys. Rev. 133, A171 (1964).  https://doi.org/10.1103/PhysRev.133.A171
  24. 24.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965).  https://doi.org/10.1103/PhysRev.140.A1133
  25. 25.
    K. Terakura, A.R. Williams, T. Oguchi, J. Kübler, Phys. Rev. Lett. 52, 1830 (1984).  https://doi.org/10.1103/PhysRevLett.52.1830
  26. 26.
    D.J. Singh, W.E. Pickett, Phys. Rev. B 44, 7715 (1991).  https://doi.org/10.1103/PhysRevB.44.7715
  27. 27.
    A. Szabo, N.S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover, New York, 1996)Google Scholar
  28. 28.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Dover, New York, 2004)Google Scholar
  29. 29.
    L.F. Mattheiss, Phys. Rev. Lett. 58, 1028 (1987).  https://doi.org/10.1103/PhysRevLett.58.1028
  30. 30.
    N.F. Mott, Metal-Insulator Transitions (Taylor and Francis, London, 1974)Google Scholar
  31. 31.
    B.J. Powell, in Computational methods for large systems: electronic structure approaches for biotechnology and nanotechnology, ed. by J.R. Reimers (Wiley, Hoboken, 2011), pp. 309–366. chap. 10, arXiv:0906.1640 [physics.chem-ph].  https://doi.org/10.1002/9780470930779.ch10. ISBN 9780470930779
  32. 32.
    A. Cabo-Bizet, A. Cabo Montes de Oca, Phys. Lett. A 373(21), 1865 (2009).  https://doi.org/10.1016/j.physleta.2009.03.018
  33. 33.
    A. Cabo-Bizet, A. Cabo Montes De Oca, Symmetry 2(1), 388 (2010).  https://doi.org/10.3390/sym2010388
  34. 34.
    V.M. Martinez Alvarez, A. Cabo-Bizet, A. Cabo Montes de Oca, Int. J. Mod. Phys. B 28(22), 1450146 (2014).  https://doi.org/10.1142/S021797921450146X
  35. 35.
    Y. Vielza, A. Cabo Montes de Oca, Revista Cubana de Física 31(2), 75 (2014)Google Scholar
  36. 36.
    A. Cabo Montes de Oca, N.H. March, A. Cabo-Bizet, Int. J. Mod. Phys. B 28(04), 1450027 (2014).  https://doi.org/10.1142/S0217979214500271
  37. 37.
    A. Cabo-Bizet, A. Cabo Montes de Oca, Fases de Mott y pseudogap a partir de un modelo simple del \(La_{2}CuO_{4}\) : cómo las fases de Mott y de pseudogap emergen de un modelo simple para las capas \(CuO_2\) (Editorial Académica Española, Saarbrücken, 2012). ISBN 9783659050541Google Scholar
  38. 38.
    J.L. Tallon, J.W. Loram, Physica C 349(1–2), 53 (2001).  https://doi.org/10.1016/S0921-4534(00)01524-0
  39. 39.
    D.M. Broun, Nat. Phys. 4(3), 170 (2008).  https://doi.org/10.1038/nphys909
  40. 40.
    F. Aryasetiawan, O. Gunnarsson, Rep. Progr. Phys. 61(3), 237 (1998).  https://doi.org/10.1088/0034-4885/61/3/002

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Física TeóricaInstituto de Cibernética, Matemática y FísicaHavanaCuba

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