Roadmap for warm dense matter physics

TL;DR

This Roadmap surveys warm dense matter (WDM) across theory, computation, and experiment, highlighting how strongly coupled, partially degenerate electrons coexisting with ions demand multi-scale, multi-physics modeling. It organizes advances into 26 sections that cover ab initio methods (PIMC, DFT/TD-DFT, Green's functions, and many-body response), experimental generation/diagnostics (DACs, laser heating, shocks, and beams), system-specific physics (hydrogen, H–He mixtures, ices, rocks, dwarfs/NS crusts), applied contexts (ICF, novel materials), and enabling tools (ML, databases, open-source software, and future facilities). A central theme is the synergy between exact or near-exact quantum methods (PIMC, GF, TD-DFT) and efficient, scalable models (AA/CM, OF-DFT, MLIPs) to predict EOS, transport, and opacities, validated by XRTS and other diagnostics. The roadmap emphasizes data-driven infrastructure, uncertainty quantification, and the development of finite-$T$ XC functionals/kernels to improve predictive capability, with a forward-looking view toward next-generation facilities and quantum-enabled computing. The work aims to deliver integrated, multi-scale predictions that inform planetary interiors, ICF, and material synthesis under extreme conditions, ultimately accelerating discovery and practical applications in WDM science.

Abstract

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations \& experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

Figures (25)

• Figure 1: Left: schematic PIMC configuration in the $x$-$\tau$ plane; the red and green paths show electrons and protons. Center: PIMC results for the electronic ITCF $F_{ee}(\mathbf{q},\tau)$ of warm dense beryllium in the $q$-$\tau$-plane (colored surface), compared to an XRTS measurement at the NIF Doeppner_nature_2023 (dashed blue) dornheim2024unraveling. Right: Shock Hugoniot curve of MgSiO$_3$ that was computed by combining PIMC and DFT-MD results into a single, consistent EOS stable. Ionization, radiation and relativistic effects were analyzed in Ref. gonzalez2020path.
• Figure 2: Overview from Ref. Bonitz_POP_2024 of different types of quantum Monte Carlo simulation methods for WDM (modified). Density, pressure and phases refer to warm dense hydrogen.
• Figure 3: Electronic density response to a 300 keV (left) and 30 MeV (right) proton traversing warm dense deuterium in a TD-DFT stopping power simulation. Arrows indicate the proton's direction of motion, and red and yellow isosurfaces bound regions where the density exceeds its initial unperturbed values (blue). TD-DFT captures both localized and extended electronic excitations created by ions in both velocity regimes.
• Figure 4: The quadratic static response function at the second harmonic $\chi^{(2,2)}(q,0)$ for the warm dense UEG at $r_s=2$ and $\Theta=1$. The green stars (green diamonds) show PIMC results for $N = 14\,(N = 20)$ electrons, and the grey stars show PIMC data for ideal fermions. The dashed blue and dotted-red lines show theoretical results within the RPA and adopting the static LFC extracted from PIMC Dornheim_JCP_2019. The solid-yellow line shows the ideal response function $\chi^{(2,2)}_0(q)$. (Reproduced from Ref. Dornheim_PhysRevRes_2021).
• Figure 5: Ab initio PIMC results for the dynamic Matsubara local field correction of the UEG at $r_s=20$ and $\Theta=1$, with $l$ the Matsubara frequency order. (Reproduced from Ref. Dornheim_PhysRevB_2024.)