Perturbation Calculation of the Uniform Electron Gas with a Transcorrelated Hamiltonian

TL;DR

This paper uses a transcorrelated Hamiltonian to perform many-body perturbation calculations on the uniform electron gas, accurately capturing the logarithmic correlation energy term and showing the method's potential for metallic systems.

Contribution

It introduces a transcorrelated approach with an optimized correlation factor to compute correlation energies, closely matching RPA results in high-density electron gas.

Findings

Second order correlation energy matches RPA's logarithmic term

Constant term is about 7% larger than RPA

Demonstrates transcorrelated method's viability for metallic systems

Abstract

With a transcorrelated Hamiltonian, we perform a many body perturbation (MBPT) calculation on the uniform electron gas in the high density regime. By using a correlation factor optimised for a single determinant Jastrow ansatz, the second order correlation energy is calculated as $\frac{1-\ln2}{\pi^{2}}\ln(r_{s})-0.05075$. This already reproduces the exact logarithmic term of the random phase approximation (RPA) result, while the constant term is roughly $7\%$ larger than the RPA one. The close agreement with the RPA method demonstrates that the transcorrelated method offers a viable and potentially efficient method for treating metallic systems.