Pair Densities in a Two-dimensional Electron Gas (Jellium) at Strong Coupling from Scattering Theory with Kukkonen-Overhauser Effective Interactions

Abstract

We present a calculation of the spin-averaged and spin-resolved pair distribution functions for a homogeneous gas of electrons moving in a plane with 2 / interactions at coupling strength s = 10. The calculation is based on the solution of a two-electron scattering problem for both parallelspin-and antiparallel-spin-pairs interacting via effective spin-dependent many-body potentials. The scattering potentials are modeled within the approach proposed by Kukkonen and Overhauser to treat exchange and correlations under close constraints imposed by sum rules. We find very good agreement with quantum MonteCarlo data for the spin-averaged pair density. We also find that short-range pairing between parallel-spin electrons is beginning to emerge in the paramagnetic fluid at this coupling strength, as a precursor of a transition to a fully spin-polarized fluid state occurring at stronger coupling.

Self-consistent scattering theory of the pair distribution function in charged Bose fluids

“…There has recently been a renewed interest in the study of g(r) for electron gas models within a two-body scattering approach stemming from work by Overhauser 4 . In brief, g(r) is obtained from the solution of a Schrdinger equation for particle-pair wave functions with effective scattering potentials which, starting from a simple electrostatic model 4,5 , have been developed into a self-consistent Hartree model 6 and into spin-dependent effective pair interactions 7 . In the present work we derive a DFT basis for such an approach and, using an earlier modelling of the effective interactions to incorporate the thermodynamic sum rules 8 , we develop a fully self-contained and self-consistent determination of g(r) and of the effective scattering potential.…”

“…We conclude, therefore, that for a Bose fluid the scattering-theory approach to the pair distribution function admits a rigorous DFT derivation, which yields Eqs. ( 6) and (7).…”

Pair distribution function in a two-dimensional electron gas

“…With decreasing dimensionality the role of exchange and correlations becomes more important and a screened Coulomb potential is insufficient to completely capture this physics. The use of self-consistent spin-dependent effective potentials has proved able to reproduce more closely the numerical results in this range of densities [2].…”

“…There has recently been a growth of interest in studying the pair distribution function, g(r ), in electron gas models [1][2][3][4], caused mainly by its relevance in non-local density functional theories [5][6][7]. The zero inter-electronic distance value, g(r = 0), also appears in the large wavevector and the high-frequency limits of the electronic charge and spin response functions [8,9].…”

Pair densities at contact in the quantum electron gas

“…A direct extension of Overhauser's model to the 2D case suffers from the difficulty that the electrical potential due to an electron plus its neutralizing Wigner-Seitz disc does not vanish outside the disc [12,13]. Furthermore, inclusion of exchange and correlation through a spin-dependent scattering potential is needed to account for the emergence of a first-neighbour shell already at relatively low values of the coupling strength in this case [14]. We report in Figure 1 the results that we have obtained from Eq.…”