Improved Equation of State for Finite-Temperature Spin-Polarized Electron Liquids on the Basis of Singwi-Tosi-Land-Sjolander Approximation

TL;DR

This paper develops an improved equation of state for finite-temperature spin-polarized electron liquids using the STLS approximation, incorporating corrections for ferromagnetic states and validating against quantum Monte Carlo data.

Contribution

It introduces a new analytic expression for the exchange-correlation free energy applicable to both paramagnetic and ferromagnetic states, enhancing accuracy over previous models.

Findings

The iSTLS formula agrees well with quantum Monte Carlo results in the paramagnetic state.

The model highlights discrepancies in ferromagnetic state evaluations, indicating need for further research.

Provides a unified approach for spin polarization in electron liquids at finite temperatures.

Abstract

An accurate expression for the exchange-correlation free energy f_{xc} of homogeneous electron fluids at finite temperatures is presented on the basis of Singwi-Tosi-Land-Sjolander (STLS) approximation. In addition to the derivation for the paramagnetic state, that for the ferromagnetic state is newly carried out in which a correction in the strong Coulomb coupling regime is incorporated into the construction of analytic expression as a function of the coupling constant and the Fermi degeneracy. The fitting formula for f_{xc} is then extended over any degree of spin polarization with the aid of available interpolation scheme. The proposed equation of state, called iSTLS formula, shows reasonable agreements with the existing quantum Monte Carlo evaluations at finite temperatures in the paramagnetic state, thus giving a consensus for the thermodynamic functions between many-body theories and computer simulations. On the other hand, the current status for the agreement among various evaluations of f_{xc} is relatively unsatisfactory in the ferromagnetic state, suggesting the necessity of further investigations.