Luttinger, Peierls or Mott? Quantum Phase Transitions in Strongly Correlated 1D Electron–Phonon Systems

Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 132)

Abstract

We analyse the complex interplay of charge, spin, and lattice degrees of freedom in one–dimensional electron systems coupled to quantum phonons. To this end, we study generic model Hamiltonians, such as the Holstein models of spinless fermions, the Holstein–Hubbard model and a Heisenberg spin-chain model with magneto-elastic interaction, by means of an unbiased numerical density–matrix renormalisation group technique. Thereby particular emphasis is placed on the Luttinger–liquid charge–density-wave, Peierls–insulator Mott-insulator, and spin–Peierls quantum phase transitions.

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References

  1. 1.
    N.F. Mott, Metal–Insulator Transitions (Taylor and Francis, London, 1990)Google Scholar
  2. 2.
    R. Peierls, Quantum theory of solids (Oxford University Press, Oxford, 1955)MATHGoogle Scholar
  3. 3.
    N. Tsuda, K. Nasu, A. Yanese, K. Siratori, Electronic Conduction in Oxides (Springer, Berlin, 1990)Google Scholar
  4. 4.
    A.R. Bishop, B.I. Swanson, Los Alamos Sci. 21, 133 (1993)Google Scholar
  5. 5.
    Y. Takada, A. Chatterjee, Phys. Rev. Lett. 67, 081102(R) (2003)ADSGoogle Scholar
  6. 6.
    H. Fehske, G. Wellein, G. Hager, A. Weiße, A.R. Bishop, Phys. Rev. B 69, 165115 (2004)CrossRefADSGoogle Scholar
  7. 7.
    M. Capone, G. Sangiovanni, C. Castellani, C. Di Castro, M. Grilli, Phys. Rev. Lett. 92, 106401 (2004)CrossRefADSGoogle Scholar
  8. 8.
    G.S. Jeon, T.H. Park, J.H. Han, H.C. Lee, H.Y. Choi, Phys. Rev. Lett. 70, 125114 (2004)ADSGoogle Scholar
  9. 9.
    R.T. Clay, R.P. Hardikar, Phys. Rev. Lett. 95, 096401 (2005)CrossRefADSGoogle Scholar
  10. 10.
    M. Tezuka, R. Arita, H. Aoki, Phys. Rev. Lett. 95, 226401 (2005)CrossRefADSGoogle Scholar
  11. 11.
    T. Holstein, Ann. Phys. (N.Y.) 8, 325 (1959)CrossRefADSGoogle Scholar
  12. 12.
    J. Hubbard, Proc. R. Soc. Lond. Ser. A 277, 237 (1964)CrossRefADSGoogle Scholar
  13. 13.
    J.K. Cullum, R.A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, vol. I and II (Birkhäuser, Boston, 1985)MATHGoogle Scholar
  14. 14.
    A. Weiße, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006)CrossRefADSGoogle Scholar
  15. 15.
    S.R. White, Phys. Rev. Lett. 69, 2863 (1992)CrossRefADSGoogle Scholar
  16. 16.
    E. Jeckelmann, H. Fehske, Riv. Nuovo Cimento 30, 259 (2007)Google Scholar
  17. 17.
    H. Fehske, A. Weiße, R. Schneider, (Eds.), Computational Many-Particle Physics, vol. 739 (Springer, Berlin Heidelberg, 2008)MATHGoogle Scholar
  18. 18.
    J.E. Hirsch, E. Fradkin, Phys. Rev. B 27, 4302 (1983)CrossRefADSGoogle Scholar
  19. 19.
    G. Benfatto, G. Gallavotti, J.L. Lebowitz, Helv. Phys. Acta 68, 312 (1995)MATHMathSciNetGoogle Scholar
  20. 20.
    H. Zheng, D. Feinberg, M. Avignon, Phys. Rev. B 39, 9405 (1989)CrossRefADSGoogle Scholar
  21. 21.
    H. Fehske, M. Holicki, A. Weiße, in Advances in Solid State Physics 40, ed. by B. Kramer (Vieweg, Wiesbaden, 2000), pp. 235–249CrossRefGoogle Scholar
  22. 22.
    R.H. McKenzie, C.J. Hamer, D.W. Murray, Phys. Rev. B 53, 9676 (1996)CrossRefADSGoogle Scholar
  23. 23.
    R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 80, 5607 (1998)CrossRefADSGoogle Scholar
  24. 24.
    G. Wellein, H. Fehske, Phys. Rev. B 58, 6208 (1998)CrossRefADSGoogle Scholar
  25. 25.
    S. Sykora, A. Hübsch, K.W. Becker, G. Wellein, H. Fehske, Phys. Rev. B 71, 045112 (2005)CrossRefADSGoogle Scholar
  26. 26.
    M. Hohenadler, G. Wellein, A.R. Bishop, A. Alvermann, H. Fehske, Phys. Rev. B 73, 245120 (2006)CrossRefADSGoogle Scholar
  27. 27.
    F.D.M. Haldane, Phys. Rev. Lett. 45, 1358 (1980)CrossRefMathSciNetADSGoogle Scholar
  28. 28.
    S. Tomonaga, Prog. Phys. Ther. 5, 544 (1950)CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    J.M. Luttinger, J. Math. Phys. 4, 1154 (1963)CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    J.L. Cardy, J. Phys. A 17, L385 (1984)CrossRefMathSciNetADSGoogle Scholar
  31. 31.
    H. Fehske, G. Wellein, G. Hager, A. Weiße, K.W. Becker, A.R. Bishop, Phys. B 359-361, 699 (2005)CrossRefGoogle Scholar
  32. 32.
    E. Jeckelmann, F. Gebhard, F.H.L. Essler, Phys. Rev. Lett. 85, 3910 (2000)CrossRefADSGoogle Scholar
  33. 33.
    E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)CrossRefADSGoogle Scholar
  34. 34.
    D. Sénéchal, D. Perez, D. Plouffe, Phys. Rev. B 66, 075129 (2002)CrossRefADSGoogle Scholar
  35. 35.
    C.E. Greffield, G. Sangiovanni, M. Capone, Eur. Phys. J. B 44, 175 (2005)CrossRefADSGoogle Scholar
  36. 36.
    E. Jeckelmann, C. Zhang, S.R. White, Phys. Rev. B 60, 7950 (1999)CrossRefADSGoogle Scholar
  37. 37.
    H. Fehske, A.P. Kampf, M. Sekania, G. Wellein, Eur. Phys. J. B 31, 11 (2003)CrossRefADSGoogle Scholar
  38. 38.
    W. Kohn, Phys. Rev. 133, A171 (1964)CrossRefMathSciNetADSGoogle Scholar
  39. 39.
    A.A. Ovchinnikov, Sov. Phys. JETP 30, 1160 (1970)ADSGoogle Scholar
  40. 40.
    H. Fehske, G. Wellein, A. Weiße, F. Göhmann, H. Büttner, A.R. Bishop, Phys. B 312–313, 562 (2002)CrossRefGoogle Scholar
  41. 41.
    N. Gidopoulos, S. Sorella, E. Tosatti, Eur. Phys. J. B 14, 217 (2000)CrossRefADSGoogle Scholar
  42. 42.
    H. Fehske, G. Hager, E. Jeckelmann, Europhys. Lett. 84, 57001 (2008)CrossRefADSGoogle Scholar
  43. 43.
    J.W. Bray, H.R. Hart Jr., L.V. Interrante, I.S. Jacobs, J.S. Kasper, G.D. Watkins, S.H. Wee, J.C. Bonner, Phys. Rev. Lett. 35, 744 (1975)CrossRefADSGoogle Scholar
  44. 44.
    M. Hase, I.Terasaki, K. Uchinokura, Phys. Rev. Lett. 70, 3651 (1993)CrossRefADSGoogle Scholar
  45. 45.
    K. Kuboki, H. Fukuyama, J. Phys. Soc. Jpn. 56, 3126 (1987)CrossRefADSGoogle Scholar
  46. 46.
    A. Weiße, G. Wellein, H. Fehske, Phys. Rev. B 60, 6566 (1999)CrossRefADSGoogle Scholar
  47. 47.
    C. Raas, A. Bühler, G.S. Uhrig, Eur. Phys. J. B 21, 369 (2001)CrossRefADSGoogle Scholar
  48. 48.
    R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 83, 408 (1999)CrossRefADSGoogle Scholar
  49. 49.
    G. Hager, A. Weiße, G. Wellein, E. Jeckelmann, H. Fehske, J. Magn. Magn. Mater. 310, 1380 (2007)CrossRefADSGoogle Scholar
  50. 50.
    K. Okamoto, K. Nomura, Phys. Lett. A 169, 433 (1992)CrossRefADSGoogle Scholar
  51. 51.
    A. Weiße, G. Hager, A.R. Bishop, H. Fehske, Phys. Rev. B 74, 214426 (2006)CrossRefADSGoogle Scholar
  52. 52.
    E. Ejima, H. Fehske, Europhys. Lett. 87, 27001 (2009)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institut für PhysikErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany
  2. 2.Regionales Rechenzentrum ErlangenUniversität ErlangenErlangenGermany

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