DMFT Method
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Figure 1. (a) Correlation energy (energy relative to paramagnetic Hartree-Fock, PMHF) as a function of atomic volume for Ce at three temperatures: DMFT (symbols) and polarized HF (dotted lines). The latter solutions, which resemble LDA+U, yield energies which approach the DMFT curves at large volume for the respective temperatures. The DMFT correlation energy is seen to bend sharply away from the polarized HF result in the region of the the observed alpha-to-gamma transition (arrows). (b) The resultant negative curvature leads to a growing depression of the total energy near V = 26-28 Å3 as temperature is decreased, consistent with an emerging double well at still lower temperatures and thus the alpha-to-gamma transition. The curves at T = 0.544 eV in (b) were shifted downwards by -0.5 eV to match the energy range. [from K. Held et. al., Phys. Rev. Lett. 87, 276404 (2001)].

Dynamical Mean Field Theory (DMFT) Method


Alex Landa and Andy McMahan

Lanthanides

Dynamical Mean Field Theory (DMFT) has recently offered a practical way to treat the critical on-site correlations which dominate the properties of many f-electron metals and f- and d-electron compounds. The fundamental approximation of the method is the assumption of a local or k-independent electron self energy; however, the essential frequency dependence is retained (thus dynamical mean field). This approximation allows for a self-consistent mapping of the full many-body problem onto an effective Anderson impurity Hamiltonian, which may then be solved by standard approximations, or by essentially exact Quantum Monte Carlo (QMC) techniques, in order to obtain the self energy. While the original applications of DMFT centered on models such as the Hubbard Hamiltonian, more exciting recent work has demonstrated the successful merger of the realism of local-density-approximation (LDA) methods with ability to treat strong electron correlations by DMFT. In this combined "LDA+DMFT" approach, LDA calculations provide the one-body part of an all-valence-orbital effective Hamiltonian which then contains all the numerical richness and material specificity characteristic of LDA methods. To this is added the correct two-body on-site Coulomb interaction, whose strength is determined by companion "constrained-occupation" LDA calculations. The resultant all-valence-orbital many-body Hamiltonian is solved by DMFT, and the system total energy taken to be Etot = ELDA + EDMFT - EmLDA. Here, ELDA is the all-electron LDA total energy, EDMFT is the DMFT energy for the valence many-body Hamiltonian, and EmLDA is the energy of an LDA-like (or model LDA, mLDA) solution of the same Hamiltonian. LDA+DMFT calculations for the lanthanide volume collapse transitions have been carried out by LLNL and collaborators (K. Held, R. Scalettar) using the rigorous QMC treatment of the self energy.

ATLAS Grand Challenge DMFT Project

The Grand Challenge project "Predictive properties of Plutonium with Dynamical Mean Field Theory," has been awarded a Tier One allocation (116,000 CPU/hrs per week for a period of one year) on the 44-TF-peak ATLAS machine at LLNL. The project is lead by two CO-PIs (A. Landa (PAT) and M. Fluss (CMLS)) with the LLNL team (A. McMahan and R. Hood) and includes a very strong international collaboration with the group of Prof. D. Vollhardt (University of Augsburg, Germany), group of Prof. V. Anisimov (Institute of Metall Physics, Russia), and Dr. R. Arita (RIKEN, Japan). This project will provide, for the first time, a highly detailed understanding of the complex electronic structure of plutonium and the features responsible for its complicated phase diagram at ambient pressure. The project will use two highly-parallelized codes: 1. The Standard Augsburg Parallelized Code (SAPC) to treat plutonium at room temperature and higher; 2. The Projective QMC Code (PQMCC) designed to treat plutonium in the cryogenic regime (down to 0K).

REFERENCES

  1. D. Vollhardt, in Correlated Electron Systems, edited by V. J. Emery (World Scientific, Singapore) 57 (1993); Th. Pruschke et al., Adv. Phys. 44, 187 (1995); A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
  2. V. I. Anisimov et al., J. Phys. Cond. Matter 9, 7359 (1997); A. I. Lichtenstein and M. I. Katsnelson, Phys. Rev. B 57, 6884 (1998); K. Held et al., Int. J. Mod Phys. B 15, 2611 (2001).
  3. K. Held, A. K. McMahan, and R. T. Scalettar, Phys. Rev. Lett. 87, 276404 (2001); A. K. McMahan, K. Held, and R. T. Scalettar, Phys. Rev. B 67, 075108 (2003); A. K. McMahan, Phys. Rev. B 72, 115125 (2005)
  4. K. Held, I. A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A. K. McMaha, R. T. Scalettar, Th. Pruschke, V. I. Anisimov, and D. Vollhardt, Phys. Stat. Sol. (b) 243, 2599 (2006).
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