Abstract
We discuss the Mott-Hubbard transition, the metal-insulator transition as a function of interaction strength U, for the half-filled Hubbard model in two numerically tractable cases: on a one-dimensional chain with nearest-neighbor hopping t’, and in the limit of infinite dimensions. In the one-dimensional model, we calculate the electric susceptibility using the Density Matrix Renormalization Group and show that the transition is infinite order, irrespective of t’ In infinite dimensions, we use the Random Dispersion Approximation to calculate the behavior of the quasiparticle weight and the single-particle gap for the transition from the paramagnetic metal to the paramagnetic insulator. Within the accuracy of our calculations, we find no evidence of the discontinuous behavior found in other approaches to the infinite-dimensional limit.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.F. Mott, Metal-Insulator Transitions, 2nd ed. (Taylor and Francis, London, 1990).
F. Gebhard, The Mott Metal-Insulator Transition, Springer Tracts in Modern Physics Vol. 137 (Springer, Berlin, 1997).
M. Fabrizio, Phys. Rev. B 54, 10054 (1996).
S. Eggert, Phys. Rev. B 54, 9612 (1996); K. Okamoto and K. Nomura, Phys. Lett. A 169, 422 (1992).
R. Arita, K. Kuroki, H. Aoki, and M. Fabrizio, Phys. Rev. B 57, 10 324 (1998).
S. Daul and R. M. Noack, Phys. Rev. B 61, 1646 (2000).
R. Resta, Phys. Rev. Lett. 80, 1800 (1998); R. Resta and S. Sorella, Phys. Rev. Lett. 82, 370 (1999).
C. Aebischer, D. Baeriswyl, and R. M. Noack, cond-mat/0006354.
A. A. Ovchinnikov, Sov. Phys. JETP 30, 1160 (1970).
C. A. Stafford and A. J. Millis, Phys. Rev. B 48, 1409 (1993).
V. Privman and M. E. Fisher, Phys. Rev. B 30, 322 (1984).
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
R. M. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).
E. R. Davidson, Comp. in Physics 7, 519 (1993).
M. J. Rozenberg, G. Moeller, and G. Kotliar, Mod. Phys. Lett. B 8, 535 (1994).
M. Caffarel and W. Krauth, Phys. Rev. Lett. 72, 1545 (1994).
G. Moeller, Q. Si, G. Kotliar, M. J. Rozenberg, and D. S. Fisher, Phys. Rev. Lett. 74, 2082 (1995).
R. Bulla, Phys. Rev. Lett. 83, 136 (1999).
J. Schlipf et al., Phys. Rev. Lett. 82, 4890 (1999).
M. Rozenberg, R. Chitra, and G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Noack, R.M., Aebischer, C., Baeriswyl, D., Gebhard, F. (2001). Studies of the Mott-Hubbard Transition in one and Infinite Dimensions. In: Bonča, J., Prelovšek, P., Ramšak, A., Sarkar, S. (eds) Open Problems in Strongly Correlated Electron Systems. NATO Science Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0771-9_36
Download citation
DOI: https://doi.org/10.1007/978-94-010-0771-9_36
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6896-0
Online ISBN: 978-94-010-0771-9
eBook Packages: Springer Book Archive