Nonlinear Electronic Density Response in Warm Dense Matter

Warm dense matter (WDM)—an extreme state with high temperatures and densities that occurs, e.g., in astrophysical objects—constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first ab initio path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.

Figure 1

Density response of the UEG for $N=14$, $r_s=2$, and $\theta =1$ with $q\approx 0.84q_F$ in dependence of the perturbation amplitude $A$ [cf. Eq. (1)]. Panel (a) shows the PIMC data for the induced density $\rho$ (green crosses), the prediction from LRT [solid red, cf. Eq. (3)], and a cubic fit [dotted blue, cf. Eq. (4)] as well as the linear component thereof (dashed black). Panel (b) shows the deviation of LRT (black squares) and the cubic fit (blue diamonds) from the PIMC data. The vertical gray dashed line corresponds to the maximum $A$ value that has been included in the fit.

Figure 2

Density response of an electron gas to an external harmonic perturbation at different conditions. Panels (a) and (b) show results for $\theta =1$ and $r_s=2$ and $r_s=6$, respectively. The top halves correspond to the cubic response function ${\chi }_3(q)$ [computed via fits, cf. Eq. (4)], and the bottom half to the (pseudo-) linear response function $\chi (q)$ from LRT [red, cf. Eq. (3)], and for different perturbation amplitudes [black and blue, cf. Eq. (5)]. Panel (c) corresponds to $r_s=2$ for $\theta =4$ (blue), $\theta =2$ (green), and $\theta =1$ (red) and shows ${\chi }_3$ and $\chi$ (from LRT) in the top and bottom half. The diamonds, stars, and crosses correspond to $N=14$, 20, and 34. The dashed curves depict the LRT prediction computed from a recent machine-learning representation [44] of the static local field correction.

Figure 3

Density response of the UEG for $N=14$ and $r_s=2$ with $q\approx 1.69q_F$ in dependence of the perturbation amplitude $A$ [cf. Eq. (1)]. Shown are PIMC data for the induced density $\rho$ for $\theta =1$ (red circles), $\theta =2$ (green crosses), and $\theta =4$ (blue diamonds), as well as the corresponding predictions from LRT [dotted black, cf. Eq. (3)].