Finite Temperature Green’s Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

We present a finite-temperature extension of the retarded cumulant Green’s function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction $W$, and improves on the $GW$ approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high $T$ while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate $T$. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.

Figure 1

FT retarded cumulant kernel ${\gamma }_k(T,\omega )$ (top); and spectral function $A_k(T,\omega )$ for the HEG (bottom) for $r_s=4$. Vertical lines in the top plot are shown at $\pm {\omega }_p$. Note the enhanced symmetry of both ${\gamma }_k$ and $A_k$ at high $T$. The inset shows a comparison of the cumulant (solid) and $GW$ (dashes) spectral functions at $k=0$ for the lowest and highest temperatures.

Figure 2

Real (top) and imaginary (bottom) parts of the quasiparticle energy correction ${\mathrm{\Delta }}_k$ for varying temperature.

Figure 3

Finite-$T$ exchange-correlation potential $v_{\mathrm{xc}}$ (top) and exchange-correlation internal energy per particle ${ϵ}_{\mathrm{xc}}$ vs $\tau =T/T_F$ (bottom) for the HEG from the cumulant expansion (blue), compared to PIMC [16] (crosses) and fits to FT-DFT [14] (red circles). Additional results are given in the Supplemental Material [47].

Figure 4

Calculated finite-$T$ Compton spectrum (solid) compared to the free-electron results (dashes) at $r_s=4$ and $q=3$ ${\mathrm{Bohr}}^{-1}$. The inset shows the difference between the effective and true temperatures ($T^{*}-T$), where $T^{*}$ is the temperature at which the free-electron calculation best matches the cumulant result at $T$.