Abstract
We discuss the Monte Carlo simulation of coupled spin-fermion systems in the context of numerical simulations of the one-dimensional Kondo lattice. We first discuss the Kondo lattice Hamiltonian itself, and then present the technique used for its simulation. We next present numerical results for the one-dimensional symmetric Kondo lattice, obtained by extrapolating in imaginary-time increment and lattice size to obtain controlled estimates for various quantities in the thermodynamic limit. In particular, we compare spin correlations with RKKY predictions and two-impurity data, and note the opening of a “Kondo gap” as the temperature is lowered.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
J.E. Hirsch, R.L. Sugar, D.J. Scalapino, and R. Blankenbecler, Phys. Rev. B 26, 5033 (1982).
R. Blankenbecler, D.J. Scalapino, and R.L. Sugar, Phys. Rev. D 24, 2278 (1981).
E.Y. Loh and J.E. Gubernatis, “Stable Numerical Simulations of Models of Interacting Electrons in Condensed Matter Physics”, to appear in Electronic Phase Transitions, edited by W. Hanke and Y.V. Kopaev (Elsevier, New York, 1991); also, E.Y. Loh and J.E. Gubernatis, to be published in Physics Reports.
See, for example, J. Kondo, Solid State Physics, edited by F. Scitz, D. Turnbull, and H. Ehrenreich (Academic, New York, 1969), Vol. 23, p
J.E. Hirsch, Phys. Rev. Lett. 53, 2327 (1984); J.E. Hirsch, Phys. Rev. B 31, 4403 (1985).
Algorithms have also been used to explore interacting impurities in infinite hosts. See, for example, J.E. Hirsch and R.M. Fye, Phys. Rev. Lett. 56, 2521 (1986), and R.M. Fye and J.E. Hirsch, Phys. Rev. B 38, 433 (19
R.T. Scalettar, to be published in Physica C; R.T. Scalettar, D.J.Scalapino, R.L. Sugar, and S.R. White, in preparation.
R.M. Fye, Phys. Rev. B 41, 2490 (1990).
See, for example, J. Kondo, in Solid State Physics, edited by F. Scitz, D. Turnbull, and H. Ehrenreich (Academic, New York, 1969), Vol. 23, p. 183.
J.R. Schrieffer and P.A. Wolff, Phys. Rev. 149, 491 (1966).
X.Y. Zhang, E. Abrahams, and G. Kotliar, preprint.
P.A. Lee, T.M. Rice, J.W. Serene, L.J. Sham, and J. W. Wilkins, Comments Condens. Matter Phys. 12, 99 (1986). We quote this general review article as a source of current work and references.
R. Jullien and P. Pfeuty, J. Phys. F 11, 353 (1981).
C. Lacroix and M. Cyrot, Phys. Rev. B 20, 1969 (1979).
R.M. Martin, Phys. Rev. Lett. 48, 362 (1982).
M.A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975), and references therein.
T.M. Rice and K. Ueda, Phys. Rev. B 34, 6420 (1986).
K. Ueda, J. Phys. Soc. Jpn. 58, 3465 (1989).
K. Yamamoto and K. Ueda, “Ground state and magnetization process of the one-dimensional Kondo lattice”, preprint.
R. Jullien and R.M. Martin, Phys. Rev. B 26, 6173 (1982).
R. Blankenbecler, J.R. Fulco, W. Gill, and D.J. Scalapino, Phys. Rev. Lett. 58, 411 (1987).
R.M. Fye, Phys. Rev. B 33, 6271 (1986); R.M. Fye and R.T. Scalettar, Phys. Rev. B 36, 3833 (1987).
R.M. Fye and J.E. Hirsch, Phys. Rev. B 40, 4780 (1989).
S.R. White, D.J. Scalapino, R.L. Sugar, E.Y. Loh, J.E. Gubernatis, and R.T. Scalettar, Phys. Rev. B 40, 506 (1989); E.Y. Loh, J.E. Gubernatis, R.T. Scalettar, S.R. White, and R.L. Sugar, “Stable matrix-multiplication algorithms for low temperature numerical simulations of fermions”, to appear in Workshop on Interacting Electrons in Reduced Dimensions, edited by D. Baeriswyl and D.K. Campbell, Plenum, New York, 1990.
The sign problem can be improved here, however, with no approximation. See R.M. Fye, “The sign problem in spin-fermion simulations: Kondo lattice results”, preprint.
R.M. Fye, J.E. Hirsch, and D.J. Scalapino, Phys. Rev. B 35, 4901 (1987).
G. Kotliar and A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986), and ref. therein.
For the nonsymmetric case.
For calculations which do treat RKKY interactions, see, for example, D.L. Cox, Phys. Rev. B 35, 4561 (1987), and references therein.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fye, R.M. (1993). Simulating Spin-Fermion Systems: Kondo Lattice Results. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics IV. Springer Proceedings in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84878-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-84878-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84880-3
Online ISBN: 978-3-642-84878-0
eBook Packages: Springer Book Archive