Frontiers of Computational Quantum Many-Body Theory

quantum many-body theory

Our group develops novel methods and concepts to tackle problems from quantum many-body theory. The focus of our research is given by the simulation and diagnostics of warm dense matter, which requires a rigorous treatment of the complex interplay of effects like Coulomb coupling, quantum degeneracy, and strong thermal excitations. In addition, we apply our methodologies to other many-body systems such as ultracold atoms and electrons in quantum dots.

Dr Tobias Dornheim

Young Investigator Group Leader

Contact

t.dornheim@hzdr.de

+49 3581 375 23 51

Center for Advanced Systems Understanding

Untermarkt 20

D-02826 Görlitz

Path integral Monte Carlo (PIMC) simulations

We have demonstrated the capability to carry out highly accurate PIMC simulations of warm dense matter without the exponential bottleneck with respect to the number of simulated electrons. This has been achieved using the controlled xi-extrapolation method that has been suggested by Xiong and Xiong [JCP 2022].

Density functional theory (DFT) simulation of warm dense matter

Linear-response time-dependent density functional theory constitutes a potentially powerful tool for the prediction of XRTS measurements. In addition to the usual XC-functional that is required for any type of DFT application, the computation of such dynamic properties needs the so-called XC-kernel as an additional input. In practice, computing an XC-kernel consistently was limited to relatively simple XC-functionals.

X-ray Thomson scattering (XRTS) diagnostics

While XRTS has emerged as a standard method of diagnostics for experiments with warm dense matter, the accuracy of the extracted system parameters such as the temperature has remained unclear.

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.

Publications

eminus — Pythonic electronic structure theory

Wanja Timm Schulze, Sebastian Schwalbe, Kai Trepte, Stefanie Gräfe - SoftwareX, Volume 29, February 2025, 102035

In current electronic structure research endeavors such as warm dense matter or machine learning applications, efficient development necessitates non-monolithic software, providing an extendable and flexible interface. The open-source idea offers the advantage of having a source code base that can be reviewed and modified by the community. However, practical implementations can often diverge significantly from their theoretical counterpart…

Dual formulation of the maximum entropy method applied to analytic continuation of quantum Monte Carlo data

Thomas Chuna, Nicholas Barnfield, Tobias Dornheim, Michael P. Friedlander, Tim Hoheisel - arXiv - Published 3 Jan 2025

Many fields of physics use quantum Monte Carlo techniques, but struggle to estimate dynamic spectra via the analytic continuation of imaginary-time quantum Monte Carlo data. One of the most ubiquitous approaches to analytic continuation is the maximum entropy method (MEM). We supply a dual Newton optimization algorithm to be used within the MEM and provide analytic bounds for the algorithm’s error…

Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations

Tobias Dornheim, Michael Bonitz, Zhandos Moldabekov, Sebastian Schwalbe, Panagiotis Tolias, Jan Vorberger - arXiv - Published 20 December, 2024

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulation results for the chemical potential of the warm dense uniform electron gas (UEG), spanning a broad range of densities and temperatures. This is achieved by following two independent routes, i) based on the direct estimation of the free energy [Dornheim \emph{et al.}, arXiv:2407.01044] and ii) using a histogram estimator in PIMC simulations with a varying number of particles…

η-ensemble path integral Monte Carlo approach to the free energy of the warm dense electron gas and the uniform electron liquid

Tobias Dornheim, Panagiotis Tolias, Zhandos Moldabekov, Jan Vorberger - arXiv - Published 18 December, 2024

We explore the recently introduced η-ensemble approach to compute the free energy directly from \emph{ab initio} path integral Monte Carlo (PIMC) simulations [T.~Dornheim \emph{et al.}, arXiv:2407.01044] and apply it to the archetypal uniform electron gas model both in the warm dense matter and strongly coupled regimes. Specifically, we present an in-depth study of the relevant algorithmic details such as the choice of the free weighting parameter and the choice of the optimum number of intermediate η-steps to connect the real, non-ideal system (η=1) with the ideal limit (η=0)…

Modeling of warm dense hydrogen via explicit real-time electron dynamics: Dynamic structure factors

Pontus Svensson, Yusuf Aziz, Tobias Dornheim, Sam Azadi, Patrick Hollebon, Amy Skelt, Sam M. Vinko, Gianluca Gregori - Phys. Rev. E 110, 055205 – Published 18 November, 2024

We present two methods for computing the dynamic structure factor for warm dense hydrogen without invoking either the Born-Oppenheimer approximation or the Chihara decomposition, by employing a wave-packet description that resolves the electron dynamics during ion evolution. First, a semiclassical method is discussed, which is corrected based on known quantum constraints, and second, a direct computation of the density response function within the molecular dynamics. The wave-packet models are compared to PIMC and DFT-MD for the static and low-frequency behavior…

From density response to energy functionals and back: An ab initio perspective on matter under extreme conditions

Zhandos Moldabekov, Jan Vorberger, Tobias Dornheim - Progress in Particle and Nuclear Physics, Volume 140, January 2025, 104144

Energy functionals serve as the basis for different models and methods in quantum and classical many-particle physics. Arguably, one of the most successful and widely used approaches in material science at both ambient and extreme conditions is density functional theory (DFT). Various flavors of DFT methods are being actively used to study material properties at extreme conditions, such as in warm dense matter, dense plasmas, and nuclear physics applications.

Green's function perspective on the nonlinear density response of quantum many-body systems

Jan Vorberger, Tobias Dornheim, Maximilian P Böhme, Zhandos Moldabekov, Panagiotis Tolias - arXiv preprint arXiv:2410.01845

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin-Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures…

Nonlocal vs Local Pseudopotentials Affect Kinetic Energy Kernels in Orbital-Free DFT

Zhandos A Moldabekov, Xuecheng Shao, Michele Pavanello, Jan Vorberger, Tobias Dornheim - arXiv preprint arXiv:2409.12625

The kinetic energy (KE) kernel, which is defined as the second order functional derivative of the KE functional with respect to density, is the key ingredient to the construction of KE models for orbital free density functional theory (OFDFT) applications. For solids, the KE kernel is usually approximated using the uniform electron gas (UEG) model or the UEG-with-gap model. These kernels do not have information about the effects from the core electrons since there are no orbitals for the projection on nonlocal pseudopotentials…