Jellium at finite temperature

Abstract

We adopt the fixed node restricted path integral Monte Carlo method within the ‘Worm algorithm’ to simulate Wigner's Jellium model at finite, non zero, temperatures using free-particle nodes of the density matrix. The new element is that we incorporate the Worm algorithm paradigm of Prokof'ev and Svistunov in the grand canonical ensemble in order to more efficiently handle the fermionic exchanges. We present results for the structure and thermodynamic properties of the ideal Fermi gas and three points for the interacting electron gas. We treat explicitly the case of the partially polarized electron gas.

GRAPHICAL ABSTRACT

Keywords:

• Jellium
• path integral Monte Carlo simulation
• worm algorithm
• restricted path integral
• fermions sign problem

Acknowledgements

We would like to thank Saverio Moroni for several relevant discussions at S.I.S.S.A. of Trieste and David Ceperley for many e-mail exchanges which has been determinant for the realisation of the new algorithm.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 This approach (which leads to the Random Phase Approximation, RPA) is approximate insofar as the potential entering the Schrödinger equation has been taken as the Hartree potential, thus neglecting exchange and correlation between an incoming electron and the electronic screening cloud.

2 The discontinuity in the momentum distribution across the Fermi surface introduces a singularity in elastic scattering processes with momentum transfer equal to $2k_{\mathrm{F}}$.