Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

Abstract

In a recent letter [Phys. Rev. Lett. 125, 085001 (2020)], Dornheim et al. have presented the first ab initio path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/fourbody correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange-correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities (rs = 0.5, . . . , 10) and temperatures (θ = 0.01, . . . , 4). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe three-and potentially even four-body correlation functions in WDM.

Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations

“…This, in turn, will give us invaluable lessons regarding the performance of different XC-functionals [37,61], and guide the development of new approaches [62][63][64][65][66]. Finally, we re-iterate the capability of our set-up to study nonlinear effects in warm dense hydrogen, which may give unprecedented insights into many-body correlation effects in WDM [41] and are known to sensitively depend on important system parameters such as the electronic temperature [67].…”

“…sponse of warm dense hydrogen. This allows us to thoroughly address a number of fundamental questions, including i) the quantification of the impact of electron-ion correlations on electronic properties, ii) the assessment of the validity range of linear response theory and the importance of nonlinear effects [28,40,41], and iii) to check widespread model assumptions about the decomposition into bound and free electrons [21]. Most notably, we present the first, highly accurate results for the XCkernel of a realistic WDM system in the static limit (i.e., ω → 0).…”

Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling

“…Naturally, the accurate theoretical description in this case will have to take into account the mode-coupling between this external potential and the XRTS probe, and the current LFC-based theory is uniquely suited for this endeavour. A second potential application of our work is given by the possibility to use the nonlinear density response as a probe for three-and even four-body correlation functions known from many-body theory [62], which might give unprecedented insights into the physical mechanisms of WDM. Finally, we mention that a general theory of the nonlinear electronic density response can be directly incorporated into many theoretical approached that have hitherto, often by necessity, been limited to LRT.…”

“…Further new results into this direction include the exploration of the straightforward relation between nonlinear effects and higher order correlation functions known from many-body theory [62] and the computation of the nonlinear density response based on imaginary-time correlation functions defined with respect of the unperturbed system [63].…”

The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory

“…( 24) below] as a starting point for an analytic continuation [83] to the dynamic structure factor S(q, Ω) [84,85,86]the key property in X-ray Thomson scattering experiments [87,88]-and related quantities [89,90]. Finally, we mention recent advances in the description of nonlinear effects in the warm dense electron gas [91,92,93,94,95], which cannot be neglected in many situations of experimental relevance, and might give rise to an improved way of diagnostics of WDM experiments [96].…”