Advanced dielectric formalism schemes for strongly coupled electron liquids
The quantum one-component plasma or jellium is generally considered to be one of the most important idealized systems in condensed matter physics, statistical mechanics and quantum chemistry. Theoretical and computational investigations have mostly focused on its ground states at high densities (relevance to metals) and its finite temperature metallic density states (relevance to warm dense matter realized in dense astrophysical objects and after ultra-fast laser heating or shock compression of metals). More recently, the investigations began to expand towards the low density finite temperature regime that is particularly challenging for theoretical approaches due to the coexistence of strong Coulomb correlations with quantum mechanical effects.
In our recent works, we proposed a novel dielectric formalism scheme that handles quantum effects at the random phase approximation (RPA) level, assumes a frequency independent local field correction and treats strong Coulomb corrections within the integral equation theory (IET) of classical liquids; including a parametrized bridge function that allows the inclusion of strong correlations beyond the hypernetted chain (HNC) level. Systematic comparison with ab initio path integral Monte Carlo simulations and other dielectric schemes in the strongly coupled electron liquid regime, revealed that our IET-based scheme leads to unprecedented agreement especially in terms of the interaction energy and that it always leads to significant improvements over the prominent HNC-based scheme also in terms of the static structure factor. However, it has been understood that, for further improvements, it is necessary to treat quantum effects beyond the RPA level. This has been most successfully achieved in a seminal manner in the qSTLS scheme, that captures beyond-RPA quantum effects by truncating the quantum BBGKY hierarchy within the Wigner representation at its first member with the introduction of a standard factorization closure that is only appropriate at weak coupling.
We have just rigorously formulated two hybrid schemes, dubbed as IET-qSTLS and HNC-qSTLS, that combine the main advantage of the IET/HNC schemes (i.e. the treatment of strong correlations) with the main advantage of the qSTLS scheme (i.e. the treatment of exchange and diffraction effects). The HNC-qSTLS and (primarily) the IET-qSTLS schemes are expected to lead to excellent agreement with simulations and substantially improve the performance of their RPA counterparts. Both hybrid schemes lead to a quite complicated set of functional equations for the static structure factor that involves an infinite summation over the bosonic Matsubara frequencies together with an implicit sextuple integral that is ultimately converted to an implicit triple integral. An iterative algorithm has already been constructed for the solution of the IET-qSTLS and the HNC-qSTLS schemes, which is based on our existing benchmarked algorithms for the bare IET, HNC and qSTLS schemes. The algorithm would need to be solved for a large number of state points in order to lead to an accurate parametrization of the exchange-correlation free energy which is the natural end product of all dielectric schemes.