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, )

4. Pair Correlation Function

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

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

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

8. “New” Techniques Backflow
López Ríos et al., submitted to Phys. Rev. E;
Zong et al., Phys. Rev. E ;
Holtzmann et al., Phys. Rev. E ;
Kwon et al., Phys. Rev. B
Three-body Jastrow terms
Larger System sizes
Ortiz et al., Phys. Rev. Lett.,
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