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: Only one independent parameter, rs, the “typical” distance between electrons. ζ is the spin polarization.

Pair Correlation Function (Qian PRB 73, 035106.)

Pair Correlation Function

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

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

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

“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 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.

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

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

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

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!

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