Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Metal-to-Nonmetal Transitions

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

  • 951 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N.F. Mott, Metal–Insulator Transitions (Taylor and Francis, London, 1990)

    Google Scholar 

  2. R. Peierls, Quantum theory of solids (Oxford University Press, Oxford, 1955)

    MATH  Google Scholar 

  3. N. Tsuda, K. Nasu, A. Yanese, K. Siratori, Electronic Conduction in Oxides (Springer, Berlin, 1990)

    Google Scholar 

  4. A.R. Bishop, B.I. Swanson, Los Alamos Sci. 21, 133 (1993)

    Google Scholar 

  5. Y. Takada, A. Chatterjee, Phys. Rev. Lett. 67, 081102(R) (2003)

    ADS  Google Scholar 

  6. H. Fehske, G. Wellein, G. Hager, A. Weiße, A.R. Bishop, Phys. Rev. B 69, 165115 (2004)

    Article  ADS  Google Scholar 

  7. M. Capone, G. Sangiovanni, C. Castellani, C. Di Castro, M. Grilli, Phys. Rev. Lett. 92, 106401 (2004)

    Article  ADS  Google Scholar 

  8. G.S. Jeon, T.H. Park, J.H. Han, H.C. Lee, H.Y. Choi, Phys. Rev. Lett. 70, 125114 (2004)

    ADS  Google Scholar 

  9. R.T. Clay, R.P. Hardikar, Phys. Rev. Lett. 95, 096401 (2005)

    Article  ADS  Google Scholar 

  10. M. Tezuka, R. Arita, H. Aoki, Phys. Rev. Lett. 95, 226401 (2005)

    Article  ADS  Google Scholar 

  11. T. Holstein, Ann. Phys. (N.Y.) 8, 325 (1959)

    Article  ADS  Google Scholar 

  12. J. Hubbard, Proc. R. Soc. Lond. Ser. A 277, 237 (1964)

    Article  ADS  Google Scholar 

  13. J.K. Cullum, R.A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, vol. I and II (Birkhäuser, Boston, 1985)

    MATH  Google Scholar 

  14. A. Weiße, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006)

    Article  ADS  Google Scholar 

  15. S.R. White, Phys. Rev. Lett. 69, 2863 (1992)

    Article  ADS  Google Scholar 

  16. E. Jeckelmann, H. Fehske, Riv. Nuovo Cimento 30, 259 (2007)

    Google Scholar 

  17. H. Fehske, A. Weiße, R. Schneider, (Eds.), Computational Many-Particle Physics, vol. 739 (Springer, Berlin Heidelberg, 2008)

    MATH  Google Scholar 

  18. J.E. Hirsch, E. Fradkin, Phys. Rev. B 27, 4302 (1983)

    Article  ADS  Google Scholar 

  19. G. Benfatto, G. Gallavotti, J.L. Lebowitz, Helv. Phys. Acta 68, 312 (1995)

    MATH  MathSciNet  Google Scholar 

  20. H. Zheng, D. Feinberg, M. Avignon, Phys. Rev. B 39, 9405 (1989)

    Article  ADS  Google Scholar 

  21. H. Fehske, M. Holicki, A. Weiße, in Advances in Solid State Physics 40, ed. by B. Kramer (Vieweg, Wiesbaden, 2000), pp. 235–249

    Chapter  Google Scholar 

  22. R.H. McKenzie, C.J. Hamer, D.W. Murray, Phys. Rev. B 53, 9676 (1996)

    Article  ADS  Google Scholar 

  23. R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 80, 5607 (1998)

    Article  ADS  Google Scholar 

  24. G. Wellein, H. Fehske, Phys. Rev. B 58, 6208 (1998)

    Article  ADS  Google Scholar 

  25. S. Sykora, A. Hübsch, K.W. Becker, G. Wellein, H. Fehske, Phys. Rev. B 71, 045112 (2005)

    Article  ADS  Google Scholar 

  26. M. Hohenadler, G. Wellein, A.R. Bishop, A. Alvermann, H. Fehske, Phys. Rev. B 73, 245120 (2006)

    Article  ADS  Google Scholar 

  27. F.D.M. Haldane, Phys. Rev. Lett. 45, 1358 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  28. S. Tomonaga, Prog. Phys. Ther. 5, 544 (1950)

    Article  MathSciNet  ADS  Google Scholar 

  29. J.M. Luttinger, J. Math. Phys. 4, 1154 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  30. J.L. Cardy, J. Phys. A 17, L385 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  31. H. Fehske, G. Wellein, G. Hager, A. Weiße, K.W. Becker, A.R. Bishop, Phys. B 359-361, 699 (2005)

    Article  Google Scholar 

  32. E. Jeckelmann, F. Gebhard, F.H.L. Essler, Phys. Rev. Lett. 85, 3910 (2000)

    Article  ADS  Google Scholar 

  33. E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)

    Article  ADS  Google Scholar 

  34. D. Sénéchal, D. Perez, D. Plouffe, Phys. Rev. B 66, 075129 (2002)

    Article  ADS  Google Scholar 

  35. C.E. Greffield, G. Sangiovanni, M. Capone, Eur. Phys. J. B 44, 175 (2005)

    Article  ADS  Google Scholar 

  36. E. Jeckelmann, C. Zhang, S.R. White, Phys. Rev. B 60, 7950 (1999)

    Article  ADS  Google Scholar 

  37. H. Fehske, A.P. Kampf, M. Sekania, G. Wellein, Eur. Phys. J. B 31, 11 (2003)

    Article  ADS  Google Scholar 

  38. W. Kohn, Phys. Rev. 133, A171 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  39. A.A. Ovchinnikov, Sov. Phys. JETP 30, 1160 (1970)

    ADS  Google Scholar 

  40. H. Fehske, G. Wellein, A. Weiße, F. Göhmann, H. Büttner, A.R. Bishop, Phys. B 312–313, 562 (2002)

    Article  Google Scholar 

  41. N. Gidopoulos, S. Sorella, E. Tosatti, Eur. Phys. J. B 14, 217 (2000)

    Article  ADS  Google Scholar 

  42. H. Fehske, G. Hager, E. Jeckelmann, Europhys. Lett. 84, 57001 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  44. M. Hase, I.Terasaki, K. Uchinokura, Phys. Rev. Lett. 70, 3651 (1993)

    Article  ADS  Google Scholar 

  45. K. Kuboki, H. Fukuyama, J. Phys. Soc. Jpn. 56, 3126 (1987)

    Article  ADS  Google Scholar 

  46. A. Weiße, G. Wellein, H. Fehske, Phys. Rev. B 60, 6566 (1999)

    Article  ADS  Google Scholar 

  47. C. Raas, A. Bühler, G.S. Uhrig, Eur. Phys. J. B 21, 369 (2001)

    Article  ADS  Google Scholar 

  48. R.J. Bursill, R.H. McKenzie, C.J. Hamer, Phys. Rev. Lett. 83, 408 (1999)

    Article  ADS  Google Scholar 

  49. G. Hager, A. Weiße, G. Wellein, E. Jeckelmann, H. Fehske, J. Magn. Magn. Mater. 310, 1380 (2007)

    Article  ADS  Google Scholar 

  50. K. Okamoto, K. Nomura, Phys. Lett. A 169, 433 (1992)

    Article  ADS  Google Scholar 

  51. A. Weiße, G. Hager, A.R. Bishop, H. Fehske, Phys. Rev. B 74, 214426 (2006)

    Article  ADS  Google Scholar 

  52. E. Ejima, H. Fehske, Europhys. Lett. 87, 27001 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, 17487, Greifswald, Germany

    Holger Fehske

  2. Regionales Rechenzentrum Erlangen, Universität Erlangen, 91058, Erlangen, Germany

    Georg Hager

Authors
  1. Holger Fehske
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georg Hager
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Holger Fehske .

Editor information

Editors and Affiliations

  1. Inst. Physik, Universität Rostock, Rostock, 18051, Germany

    Ronald Redmer

  2. FB Physikalische Chemie, Universität Marburg, Hans-Meerwein-Str., Marburg, 35032, Germany

    Friedrich Hensel

  3. Inst. Physik, Universität Rostock, Rostock, 18051, Germany

    Bastian Holst

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fehske, H., Hager, G. (2010). Luttinger, Peierls or Mott? Quantum Phase Transitions in Strongly Correlated 1D Electron–Phonon Systems. In: Redmer, R., Hensel, F., Holst, B. (eds) Metal-to-Nonmetal Transitions. Springer Series in Materials Science, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03953-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03953-9_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03952-2

  • Online ISBN: 978-3-642-03953-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation