The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids and much more. Accurate thermodynamic data for the UEG are an essential ingredient for many-body theories, in particular, density functional theory. Recently, first-principle restricted path integral Monte Carlo results became available which, however, due to the fermion sign problem, had to be restricted to moderate degeneracy, i.e. low to moderate densities with rs =r/aB 1. Here we present novel first-principle configuration PIMC results for electrons for rs ≤ 1. We also present quantum statistical data within the e 4 -approximation that are in good agreement with the simulations at small to moderate rs. [11,12]. Besides, the electron component is of crucial importance for understanding the properties of atoms, molecules and existing and novel materials. The most successful approach has been density functional theory (DFT)-combined with an approximation for the exchange-correlation potential. Its success is based on the availability of accurate zero temperature data for the UEG which is obtained from analytically known limiting cases combined with first-principle quantum Monte Carlo data [13].In recent years more and more applications have emerged where the electrons are highly excited, e.g. by compression of the material or by electromagnetic radiation (see above), which require to go beyond zero temperature DFT. This has led to an urgent need for accurate thermodynamic data of the UEG at finite temperature. One known limiting case is the highly degenerate ideal Fermi gas (IFG), and perturbation theory results around the IFG, starting with the Hartree-Fock and first order correlation corrections (Montroll-Ward) [14,15] [27]. It is well known that fermionic PIMC simulation in continuous space suffer from the fermion sign problem (FSP) which is known to be NP hard [28]. This means, with increasing quantum degeneracy, i.e. increasing parameter χ = nλ 3 DB , which is the product of density and thermal DeBroglie wave length, λ, the simulations suffer an exponential loss of accuracy. RPIMC formally avoids the FSP by an additional assumption on the nodes of the density matrix, however, it also cannot access high densities [29], r s < 1 [r s =r/a B , wherer is the mean interparticle distance, n −1 = 4πr 3 /3 and a B the Bohr radius]. Also, the quality of the simulations around r s = 1, at low temperatures Θ = k B T /E F ≤ 0.125 [E F is the Fermi energy] is unknown. However, this leaves out the high-density range that is of high importance, e.g. for deuterium-tritium implosions at NIF where mass densities of 400 gcm −3 (up to 1596 gcm −3 ) have recently been reported [9] (are expected along the implosion path [8]), corresponding to r s ≈ 0.24 (r s = 0.15), see Fig. 1.The authors of Ref.[27] also performed DPIMC simulations which confirmed that, for Θ < 0.5 and r s 4, these simulations are practically not possible, see Fig. 1. We also mention independent recent DPIMC ...

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressed e.g. by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at nite temperature|a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently several breakthroughs have been achieved in the eld of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulations of a nite model system (30 : : : 100 electrons) is possible that avoid any simplifying approximations such as xed nodes [Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available that have an unprecedented accuracy on the order of 0:1%. Here we present an overview on these results and discuss limitations and future directions

A novel path integral Monte Carlo (PIMC) approach for correlated many-particle systems with arbitrary pair interaction in continuous space at low temperatures is presented. It is based on a representation of the N -particle density operator in a basis of (anti-)symmetrized N -particle states (configurations of occupation numbers). The path integral is transformed into a sum over trajectories with the same topology and, finally, the limit of M → ∞, where M is the number of high-temperature factors, is analytically performed. This yields exact expressions for the thermodynamic quantities and allows to perform efficient simulations for fermions at low temperature and weak to moderate coupling. Our method is expected to be applicable to dense quantum plasmas in the regime of strong degeneracy where conventional PIMC fails due to the fermion sign problem.

In a recent letter [P.K. Shukla and B. Eliasson, Phys. Rev. Lett. 108, 165007 (2012)] the discovery of a new attractive force between protons in a hydrogen plasma was reported that would be responsible for the formation of molecules and of a proton lattice. Here we show, based on ab initio density functional calculations and general considerations, that these predictions are wrong and caused by using linearized quantum hydrodynamics beyond the limits of its applicability.

The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here, we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.