Remaining problems in the Homogeneous Electron Gas Graham

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 2 D 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 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.

Results for PCF (anti-parallel spins) VMC, 162 electrons, rs=3. 0, ζ=0. 0

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