Frontiers of Computational Quantum Many-Body Theory

Linear and nonlinear density response theory


The estimation of nonlinear response properties of interacting quantum many-body systems has remained limited to a few model cases due to the required very high computational effort.

To overcome this bottleneck, we have developed a new framework for the computation of a variety of nonlinear response functions, which is based on the estimation of imaginary-time many-body correlation functions. It gives one access to the full wavenumber dependence of the nonlinear response from a single simulation of the unperturbed system.

In practice, this results in a reduction of compute time by several orders of magnitude, enabling the systematic study of nonlinear properties of complex systems for the first time. In addition, the derived hierarchy that relates many-body correlations to nonlinear responses gives new insights into a number of effects such as the nonlinear coupling of several external perturbations.

Linear response theory is one of the most powerful concepts in quantum many-body theory, in general, and WDM theory, in particular. It is at the heart of modeling XRTS measurements, and gives one access to a wealth of interesting material properties such as electrical and thermal conductivities, opacity, and stopping power. In addition, our PIMC and DFT simulations also give us access to a wide class of nonlinear response properties, which play an important role for experiments with high-intensity laser beams and for the description of strongly coupled systems.

The central role of linear-response theory (LRT) in the description of nonideal quantum many-body systems such as warm dense matter or ultracold atoms can hardly be overstated. For example, the dynamic linear density response function gives one direct access to the dynamic structure factor, which is the key property in XRTS experiments. In addition, LRT is connected to a multitude of transport properties such as the dynamic dielectric function, conductivity, and stopping power. In our group, we use cutting-edge path integral Monte Carlo (PIMC) and density functional theory (DFT) simulations to estimate linear-response properties of warm dense matter, and other applications.

A related topic that has attracted considerable interest over the last years is the study of nonlinear response properties. These become important when a system is subject to a strong external perturbation such as a high-intensity laser beam, and also enter the theoretical description of material properties such as effective potentials and the stopping power. The most direct way to study nonlinear response properties is indeed the dedicated simulation of a strongly perturbed system to explicitly measure its response. While being formally exact, this approach requires multiple independent simulations to estimate a nonlinear response function for a single wavenumber at a given combination of density and temperature. A more elegant alternative is given by the estimation of higher-order imaginary-time correlation functions, which give one access to the full wavenumber dependence of the nonlinear response from a single simulation of the unperturbed system. The investigation of a variety of nonlinear response properties of real WDM systems, and their impact on the modeling of material properties, will be pursued in future works.