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

Abstract

We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W and improves excited state properties compared to 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 regime, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small. In addition, the spectral function broadens and damping increases with temperature, blurring the usual quasi-particle picture. Similarly Compton scattering exhibits substantial many-body corrections that persist at normal densities and intermediate T . Results for exchange-correlation energies and potentials are in good agreement with existing theories and finite-temperature DFT functionals. Finite temperature (FT) effects in electronic systems are both of fundamental interest and practical importance. These effects vary markedly depending on whether the temperature T is larger or smaller than the Fermi temperature T F (typically a few eV). At "cool" temperatures, where T is much smaller than T F , electrons are nearly degenerate, and Fermi factors and excitations such as phonons dominate the thermal behavior [1][2][3]. In contrast thermal occupations become nearly semi-classical and electronic excitations such as plasmons become important in the warm-dense-matter (WDM) regime, where T is of order T F or larger, and condensed matter is partially ionized. Recently there has been considerable interest in both experimental and theoretical investigations of WDM for applications ranging from laser-shocked systems and inertial confinement fusion to astrophysics [4,5]. Many of these studies focus on equilibrium thermodynamic properties, e.g., using the FT generalization of density functional theory (DFT) [6][7][8]. Although in principle, FT DFT is exact [9][10][11], practical applications require exchange-correlation functionals which must be approximated, e.g., by constrained fits [12] to theoretical electron gas calculations [8,[13][14][15][16][17]. However, these approaches have various limitations. First, many materials properties such as optical and x-ray spectra depend on quasi-particle or excited-state effects. For example, band-gaps depend on quasi-particle energies, and calculations of x-ray spectra [18] and Compton scattering require correlation corrections [19]. Although methods like quantum Monte-Carlo and the random phase approximation (RPA) can provide accurate correlation energies, they are not directly applicable to such excited state properties. Secondly, currently available exchangecorrelation functionals can exhibit unphysical behavior outside the range of validity of theoretical data [20]. On the other hand Green's function (GF) methods within...

Ab initio simulation of warm dense matter

“…Naturally, the straightforward evaluation of F (q, t) requires real time-dependent simulations [174][175][176], for which, presently an exact simultaneous treatment of exchange-correlation, thermal, and degeneracy effects is not possible. Therefore, previous results [155,174,[177][178][179][180][181] were based on partly uncontrolled approximations, the quality of which had remained unclear.…”

“…A fifth important application of the ab initio data for S(q, ω) is that they unambiguously allow us to benchmark previous approximations [172,174,176,177], which are commonly used for WDM research. For example, Dornheim et al [186] have reported that RPA exhibits significant inaccuracies even at relatively moderate coupling, r s = 2 and θ = 1, where electronic correlation effects had often been assumed to play a minor role.…”

Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

“…Our new data for S(q, ω) can also be used to benchmark approximate methods for the description of quantum dynamics at finite temperature, such as nonequilibrium Green functions [122][123][124][125] and the method of moments by Tkachenko and co-workers [126][127][128].…”

Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime inSrTiO3

“…We implement and employ a retarded cumulant approach [35,36] to compute the electron spectral function at finite temperature. The retarded cumulant approach [see Eq.…”

“…We focus on the electron spectral function in cubic SrTiO 3 above 110 K. Leveraging our recently developed approach [29], which combines density functional theory (DFT), its linear response extension [33] and the temperature dependent effective potential (TDEP) method [34], we compute the band structure, lattice vibrations and e-ph interactions for all phonon modes, including the soft modes due to the lattice anharmonicity (see Appendix B). Using these quantities, we calculate the spectral function using a retarded cumulant formalism [35,36]. The retarded cumulant approach is based on an exponential ansatz for the retarded Green's function of an electronic state |nk (with band index n and momentum k) in the time domain:…”