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Quantum Monte Carlo Simulations of Disordered Magnetic and Superconducting Materials

Published online by Cambridge University Press:  10 February 2011

R. T. Scalettar ,
P. J. H. Denteneer ,
C. Huscroft ,
A. Mcmahan ,
R. Pollock ,
M. Randeria ,
N. Trivedi ,
M. Ulmke  and
G. T. Zimanyt
R. T. Scalettar
Affiliation:
Physics Department, University of California, Davis, CA 95616
P. J. H. Denteneer
Affiliation:
Lorentz Institute, Leiden University, 2333 CA Leiden, The Netherlands
C. Huscroft
Affiliation:
Physics Department, University of California, Davis, CA 95616
A. Mcmahan
Affiliation:
Lawrence Livermore National Laboratory P. O. Box 808, Livermore, CA 94551
R. Pollock
Affiliation:
Lawrence Livermore National Laboratory P. O. Box 808, Livermore, CA 94551
M. Randeria
Affiliation:
Theor. Phys. Group, Tata Institute of Fundamental Research, Bombay 400005, India
N. Trivedi
Affiliation:
Theor. Phys. Group, Tata Institute of Fundamental Research, Bombay 400005, India
M. Ulmke
Affiliation:
Theor. Phys. III, Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany
G. T. Zimanyt
Affiliation:
Physics Department, University of California, Davis, CA 95616
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Abstract

Over the last decade, Quantum Monte Carlo (QMC) calculations for tight binding Hamiltonians like the Hubbard and Anderson lattice models have made the transition from addressing abstract issues concerning the effects of electron-electron correlations on magnetic and metal-insulator transitions, to concrete contact with experiment. This paper presents results of applications of “determinant” QMC to systems with disorder such as the conductivity of thin metallic films, the behavior of the magnetic susceptibility in doped semiconductors, and Zn doped cuprate superconductors. Finally, preliminary attempts to model the Kondo volume collapse in rare earth materials are discussed.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 491: Symposium R – Tight Binding Approach to Computational Materials Science , 1997 , 155
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

1. Blankenbecler, R., Scalapino, D.J., and Sugar, R.L., Phys. Rev. D24, 2278 (1981).Google Scholar
2. Scalapino, D.J., Physics Reports 250, 330 (1995);Google Scholar
Dagotto, E., Rev. Mod. Phys. 66, 763 (1994).Google Scholar
3. Trivedi, N., Scalettar, R.T., and Randeria, M., Phys. Rev. B54, 3756 (1996).Google Scholar
4. Ulmke, M. and Scalettar, R.T., Phys. Rev. B55, 4149 (1997).Google Scholar
5. Denteneer, P. J. H., Ulmke, M., Scalettar, R. T., Zimanyi, G. T., Physica A, to appear.Google Scholar
Ulmke, M., Denteneer, P. J. H., Scalettar, R. T., Zimanyi, G. T., unpublished.Google Scholar
6. Huscroft, C., McMahan, A., Scalettar, R.T., work in progress.Google Scholar
7. See review article by Hebard, A. F., in “Strongly Correlated Electronic Systems” edited by Bedell, K. S., Wang, Z., Meltzer, D. E., Balatsky, A. V., and Abrahams, E., (Addison-Wesley, 1994).Google Scholar
8. For a brief review, see Cha, M., Fisher, M.P. A., Girvin, S.M., Wallin, M., and Young, A.P., Phys. Rev. B44, 6883 (1991), and the references cited therein.Google Scholar
9. Krauth, W., Trivedi, N. and Ceperley, D. M., Phys. Rev. Lett. 67, 2307 (1991).Google Scholar
Sorensen, E. S., Wallin, M., Girvin, S. M., and Young, A. P., Phys. Rev. Lett. 69, 828 (1992).Google Scholar
Runge, K.J., Phys. Rev. B45, 13136 (1992).Google Scholar
Batrouni, G.G., Larson, B., Scalettar, R.T., Tobochnik, J., and Wang, J., Phys. Rev. B48, 9628 (1993).Google Scholar
10. For a recent review, see Belitz, D. and Kirkpatrick, T.R., Rev. Mod. Phys. 66, 261 (1994).Google Scholar
11. Bulaevskii, L.N. et. al., Zh. Eksp. Teor. Fiz. 62, p. 725 (1972) [Sov. Phys. JETP 35, 384 (1972)]; andGoogle Scholar
Azvedo, L.J. and Clark, W.G., Phys. Rev. B16, 3252 (1977).Google Scholar
12. Azuma, M., Fujishiro, Y., Takano, M., Ishida, T., Okuda, K., Nohara, M., and Takagi, H. (to be published);Google Scholar
Nohara, M., Takagi, H., Azuma, M., Fujishiro, Y., and Takano, M. (to be published).Google Scholar
13. Xiao, G. et al., Phys. Rev. Lett. 60, 1466 (1988);Google Scholar
Keimer, B. et al., Phys. Rev. B 45, 7430 (1992);Google Scholar
Mahajan, A. V., Alloul, H., Collin, G., and Marucco, J. F., Phys. Rev. Lett. 72, 3100 (1994).Google Scholar
14. Martins, G.B., Laukamp, M., Riera, J., and Dagotto, E., Phys. Rev. Lett. 78, 3563 (1997).Google Scholar
15. Johansson, B., Philos. Mag. 30, 469 (1974).Google Scholar
16. Allen, J.W. and Martin, R.M., Phys. Rev. Lett. 49, 1106 (1982); andGoogle Scholar
Lavagna, M., Lacroix, C., and Cyrot, M., Phys. Lett. 90A, 210 (1982).Google Scholar
17. While we have used the term “site” for the indices i and j, these can in fact also label different orbitals. From a technical viewpoint, the determinant QMC algorithm treats distinct sites and orbitals in precisely the same way. They differ only in the Hamiltonian itself, that is in the choice of t ij, U i, and μi.Google Scholar
18. Trotter, H.F., Proc. Am. Math. Soc. 10, 545 (1959); andGoogle Scholar
Suzuki, M., Phys. Lett. 113A, 299 (1985).Google Scholar
19. Naively the algorithm should scale as the fourth power of the number of sites N, since for each move of one of the NL Hubbard-Stratonovich fields, a calculation of the determinant requires N 3 operations. However, a trick reduces this by one power of N.Google Scholar
20. White, S.R., Scalapino, D.J., Sugar, R.L., Loh, E.Y. Jr, Gubernatis, J.E., and Scalettar, R.T., Phys. Rev. B40, 506 (1989).Google Scholar
21. Metzner, W. and Vollhardt, D., Phys. Rev. Lett. 62, 324 (1989);Google Scholar
for a review see Vollhardt, D., in Correlated Electron Systems, edited by Emery, V. J. (World Scientific, Singapore, 1993), p. 57;Google Scholar
Georges, A., Kotliar, G., Krauth, W., and Rozenberg, M., Rev. Mod. Phys. 68, 13 (1996);Google Scholar
Jarrell, M., Phys. Rev. Lett. 69, 168 (1992); andGoogle Scholar
Pruschke, T., Jarrell, M., and Freericks, J. K., Adv. Phys. 44, 187 (1995).Google Scholar
22. Vekic, M. and White, S.R., Phys. Rev. B47, 1160 (1993).Google Scholar
23. Jarrell, M. and Gubernatis, J. E., Phys. Rep. 269, 133 (1996).Google Scholar
24. Gebhard, F., The Mott Metal-Insulator Transition, Springer Tracts in Modern Physics, vol. 137 (Springer, Heidelberg, 1997).Google Scholar
25. Milovanovic, M., Sachdev, S., and Bhatt, R.N., Phys. Rev. Lett. 63, 82 (1989);Google Scholar
Sandvik, A.W., Scalapino, D.J., and Henelius, P., Phys. Rev. B50, 10474 (1994); andGoogle Scholar
Kirkpatrick, T.R. and Belitz, D., Phys. Rev. Lett. 76, 2571 (1996).Google Scholar