Efficient formalism for warm dense matter simulations

Simulation of warm dense matter requires computational methods that capture both quantum and classical behavior efficiently under high-temperature, high-density conditions. Currently, density functional theory molecular dynamics is used to model electrons and ions, but this method's computational cost skyrockets as temperatures and densities increase. We propose finite-temperature potential functional theory as an in-principle-exact alternative that suffers no such drawback. We derive an orbital-free free energy approximation through a coupling-constant formalism. Our density approximation and its associated free energy approximation demonstrate the method's accuracy and efficiency.

Figure 1

Shortcomings of the TF approximation in the WDM regime: Total density of five particles in the potential $v\left(x\right)=-2{sin}^2(\pi x/10)$ within a box (of size 10 a.u.) at $\mathrm{\Lambda }=\tau /\mu =0.93$. Compare the exact density (solid black curve) with our PFA (dashed red curve) derived in Eq. (11), which is basically on top of the exact result. On the other hand, the TF approximation (dotted green curve) and conventional (second-order) gradient expansion (short-dashed blue, GEA2) capture the general qualitative features but completely miss the quantum oscillations. We also show the corresponding exact density at zero temperature (light blue shaded area), with its pronounced oscillations that smooth as temperatures rise.

Figure 2

Residual kentropic density of five particles in the same potential as in Fig. 1 in the WDM regime. Our PFA (solid red curve) derived in Eq. (11) is on top of the exact result (solid black curve). TF (dotted green curve) and its gradient correction (short-dashed blue, GEA2), on the other hand, follow the general trend as expected but miss quantitative details.