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Remaining problems in the Homogeneous Electron Gas

Remaining problems in the Homogeneous Electron Gas. Graham Spink and Richard Needs, TCM, University of Cambridge. Homogeneous Electron Gas. Electrons move in uniform, positive background potential: Used in Local Density Approximation in DFT:

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Remaining problems in the Homogeneous Electron Gas

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  1. Remaining problems in the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge

  2. Homogeneous Electron Gas • Electrons move in uniform, positive background potential: • Used in Local Density Approximation in DFT: • Only one independent parameter, rs, the “typical” distance between electrons. ζ is the spin polarization.

  3. Pair Correlation Function (Qian PRB 73, 035106.)

  4. Pair Correlation Function

  5. Structure Factor Gori-Giorgi, Sacchetti and Bachelet, PRB 61, 7353

  6. Momentum Density Gori-Giorgi and Ziesche, PRB 66, 235116

  7. Effective Mass in 2D Tan et al., Phys. Rev. Lett. 94, 016405

  8. “New” Techniques • Backflow López Ríos et al., submitted to Phys. Rev. E; Zong et al., Phys. Rev. E 66 036703; Holtzmann et al., Phys. Rev. E 68 046707; Kwon et al., Phys. Rev. B 58 6800. • Three-body Jastrow terms Holtzmann et al., Phys. Rev. E 68 046707; Kwon et al., Phys. Rev. B 58 6800. • Larger System sizes Ortiz et al., Phys. Rev. Lett., 82 5317. • Different treatment of finite-size effects Chiesa et al., submitted to Phys. Rev. Lett.

  9. Results for PCF VMC, 162 electrons, rs=3.0, ζ=0.0 PCF (anti-parallel spins)

  10. Results for Momentum Density(1) VMC, 162 electrons, rs=3.0, ζ=0.0

  11. Results for Momentum Density(2) VMC, 162 electrons, rs=3.0, ζ=0.0

  12. Next Steps • Investigate larger systems, timesteps etc with backflow, three-body terms etc • Study rs=0.5, 1, 2, 3, 5, 10, 20, 30, 40; ζ=0,1. • Consider fitting procedures and infinite size extrapolation methods. • Compare with existing studies • …and hopefully answer questions posed above!

  13. Results for PCF VMC, 162 electrons, rs=3.0, ζ=0.0

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