Abstract
We study the static screening in a Hubbard-like model using fixed-node diffusion Monte Carlo. We find that the random phase approximation is surprisingly accurate even for metallic systems close to the Mott transition. As a specific application we discuss the implications of the efficient screening for the superconductivity in the doped Fullerenes. In the Monte Carlo calculations we use trVAl functions with two Gutzwiller-type parameters. To deal with such trVAl functions, we introduce a method for efficiently optimizing the Gutzwiller parameters, both in varVAtional and in fixed-node diffusion Monte Carlo.
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References
Gunnarsson, O., Koch, E., and Martin, R.M. (1996) Mott transition in degenerate Hubbard models: Application to doped Fullerenes, Phys. Rev. B 54, R11026.
Gunnarsson, O. (1997) Superconductvity in Fullendes, Rev. Mod. Phys. 69, 575–606.
Gunnarsson, O., Zwicknagl G. (1992) Coulomb PseudopotentVAl, Screening and Superconductvity in C60 Phys. Rev. Lett. 69, 957–960; Gunnarsson, O., Rainer, D., Zwicknagl, G.(1992) Screened interaction and Coulomb pseudopotentVAl in C6o Int. J. Mod. Phys. 6, 3993–4005
Koch, E., Gunnarsson, O., Martin, R.M. (1999) Screening, Coulomb pseudopotentVAl, and Superconductvity in alkali-doped Fullerenes, preprint cond-mat/9902241
Erwin, S. C. (1993) Electronic Structure of the Alkali-Intercalated Fullendes, Endohedral Fullerenes, and Metal-Adsorbed Fullerenes, in W. E. Billups and M. A. Ciufolini (Eds.), Buckminsterfullerenes, ICH Publishers, New York, pp. 217–253.
Löwdin, P. O. (1951) A Note on the Quantum-Mechanical Perturbation Theory, J. Chem. Phys. 19, 1396–1401.
see e.g. Inversion by Partitioning, in W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Ietterling, Numerical Recipes in Fortran: The Art of Scientific Computing, Cambridge University Press, 1992, p. 70.
Gunnarsson, O., Satpathy, S., Jepsen, O., and Andersen, O. K. (1991) Orientation of C60 Clusters in Solids, Phys. Rev. Lett. 67, 3002; Satpathy, S., Antropov, I. P., Andersen, O. K., Jepsen, O., Gunnarsson, O., and Liechtenstein, A. I. (1992) Conduction-band structure of alkali-metal-doped C60 Phys. Rev. B 46, 1773.
Gunnarsson, O., Erwin, S. C., Koch, E., and Martin, R. M. (1998) Role of alkali atoms in A4C60 Phys. Rev. B 57, 2159.
Antropov, I. P., Gunnarsson, O., and Jepsen, O. (1992) Coulomb integrals and model Hamiltonvans for C60 Phys. Rev. B 46, 13647.
Brühwiler, P. A., Maxwell, A. J., Nilsson, A., Mårtensson, N., and Gunnarsson, O. (1993) Auger and photoelectron study of the Hubbard U in C60, K3C60, and K6C6o Phys. Rev. B 48, 18296.
Lof, R. W., van Veenendaal, M. A., Koopmans, B., Jonkman, H. T. and Sawatzky, G. A. (1992) Band Gap, Excitons, and Coulomb interaction in solid C6o, Phys. Rev. Lett. 68, 3924.
Mazin, I.I., RashkeeI, S.N., Antropov, I.P., Jepsen, O., Liechtenstein, A.I., and Andersen O.K. (1992) QuantitatiIe theory of Superconductvity in doped C60 Phys. Rev. B 45, 5114.
Hedin, L., and LundqXIst, S. (1969) Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids, in H. EhrenRevch, D. Turnbull and F. Seitz (Eds.), Solid State Physics 23, Academic Press, New York, pp. 1–181; Moroni, S., Ceperley, D.M., and Senatore, G. (1995) Static Response and Local Field Factor of the Electron Gas, Phys. Rev. Lett. 75, 689.
Ebbesen, T.W., Tsai, J.S., Tanigaki, K., Hiura, H., Shimakawa, Y., Kubo, Y., Hirosawa, I., Mizuki, J. (1992), Physica C 203, 163; Burk, B., Crespi, I.H., Zettl, A., Cohen, M.L. (1994), Phys. Rev. Lett. 72, 3706.
Gutzwiller, M. C.(1963) Effect of correlation on the ferromagnetism of transition metals, Phys. Rev. Lett. 10, 159.
Horsch, P. and Kaplan, T.A. (1983) Exact and Monte Carlo studies of Gutzwiller’s state for the localised-electron limit in one dimension, J. Phys. C 16, L1203;Metropolis, N., Rosenbluth, A. W., Rosenbluth, N. M., Teller, A. H., and Teller, E. (1953) Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21, 1087
Ceperley, D. M., Chester, G. I., and Kalos, M. H. (1977) Monte Carlo simulation of a many-Fermion study, Phys. Rev. B 16, 3081; Umrigar, C. J., Wilson. K. G., and Wilkins, J. W. (1988) Optimized TrVAl Wave Functions for Quantum Monte Carlo Calculations, Phys. Rev. Lett. 60, 1719 Koch, E., Gunnarsson, O., and Martin, R.M (1999) Optimization of Gutzwiller Wavefunctions in Quantum Monte Carlo, preprint, cond-mat/9903070
Trivedi, N. and Ceperley, D. M. (1989) Green-function Monte Carlo study of quantum antiferromagnets, Phys. Rev. B 40, 2737.
ten Haaf, D. F. B., van Bemmel, H. J. M., van Leeuwen, J. M. J., and van Saarloos, W. (1994) Fixed-node quantum Monte Carlo method for lattice Fermions, Phys. Rev. Lett. 72, 2442; ten Haaf, D. F. B., van Bemmel, H. J. M., van Leeuwen, J. M. J., van Saarloos, W. and Ceperley, D. M. (1995) Proof for an upper bound in fixed-node Monte Carlo for lattice Fermions, Phys. Rev. B 51, 13039 Calandra, M., Sorella, S. (1998) Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers, Phys. Rev. B 57, 11446; Cosentini, A.C., Capone, M., Guidoni, L., and Bachelet, G.B. (1998) Phase separation in the 2D Hubbard model: a fixed-node quantum Monte Carlo study, Phys. Rev. B 58, R14685.
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Koch, E., Gunnarsson, O., Martin, R.M. (2000). Screening of a Point Charge: A Fixed-Node Diffusion Monte Carlo Study. In: Landau, D.P., Lewis, S.P., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics XII. Springer Proceedings in Physics, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59689-6_3
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DOI: https://doi.org/10.1007/978-3-642-59689-6_3
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