Coulomb bridge function and the pair-distribution functions of the two-dimensional electron liquid in the quantum regime

Abstract

The electron-electron pair-distribution functions (PDFs) of the two-dimensional (2D) electron fluid in the quantum regime (at $T=0$) are calculated using a classical-map-hypernetted-chain scheme and compared with currently available quantum Monte Carlo (QMC) simulations in the coupling range ${r}_{s}=1$ to 50. We iteratively extract the bridge function of the ``equivalent'' classical 2D liquid in the quantum regime. These bridge functions $B(r)$ are relatively insensitive to spin-polarization effects. The structure of the bridge functions changes significantly for ${r}_{s}>6$, suggesting the onset of strongly correlated clusters. The new $B(r)$, appropriate for the long-range Coulomb potential, can be used to replace the hard-sphere $B(r)$ previously used in these calculations. They provide accurate classical representations of the QMC-PDFs even at very strong coupling, and probably at finite-$T$ near $T=0$.