A configuration interaction approach to solve the Anderson impurity model; applications to elemental Ce

TL;DR

We present a configuration interaction impurity solver for dynamical mean-field theory that delivers real-frequency Green's functions with improved efficiency over exact diagonalization, enabling practical DMFT studies on modest hardware and providing an open-source implementation. The solver is demonstrated on elemental Cerium across the γ-, α-, and ε-phases, revealing a localization-to-itinerancy trend and a Mott-like transition between γ- and ε-Ce interrupted by α-Ce's Kondo screening. The α phase exhibits a strong Kondo resonance and Hubbard features, the γ phase remains largely localized, and ε behaves band-like with modest correlation effects; comparisons with CT-QMC show qualitative agreement, while the CI approach offers a complementary, sign-problem-free alternative with direct real-frequency access. Overall, the work supports using CI-based impurity solvers for realistic multi-orbital DMFT problems, with the added benefit of open-source availability and potential laptop-scale computations.

Abstract

Accurate calculations of strongly correlated materials remain a formidable challenge in condensed matter physics, particularly due to the computational demand of conventional methods. This paper presents an efficient solver for dynamical mean field theory using configuration interaction (CI). The method is shown to have improved efficiency compared to traditional, exact diagonalization approaches. Hence, it provides an accessible, open-source alternative that can be executed on standard laptop computers or on supercomputers. The solver is demonstrated on cerium in the $γ$-, $α$- and $ε$-phases. An analysis of how the electronic structure of Ce evolves as function of lattice compression is made. It is argued that the electronic structure evolves from a localized nature of the 4f shell in $γ$-Ce to an essentially itinerant nature of the 4f shell of $ε$-Ce. The transition between these two phases, as function of compression, can hence be seen as a Mott transition. However, this transition is intercepted by the strongly correlated $α$-phase of elemental Ce, for which the 4f shell forms a Kondo singlet.

Figures (10)

• Figure 1: Experimental and theoretical spectral function of $\alpha-$Ce for occupied states (left figure) and unoccupied states (right figure). Experimental data are from Ref.wieliczka_high-resolution_1984. The intensity difference between unoccupied and occupied states was chosen to represent the occupation of available states.
• Figure 2: Experimental and theoretical spectral function of $\gamma-$Ce for occupied states (left figure) and unoccupied states (right figure). Experimental data are from Ref.wuilloud_electronic_1983. The intensity difference between unoccupied and occupied states was chosen to represent the occupation of available states.
• Figure 3: $\alpha-$Ce: Comparison of CT-QMC total spectral function OE10 with this work (upper panel) and the $4f$ projected results (lower panel). For details of the calculations see main text.
• Figure 4: $\gamma-$Ce: Comparison of CT-QMC total spectral function OE10 with this work (upper panel) and the $4f$ projected results (lower panel). For details of the calculations see main text.
• Figure 5: Energy dispersion of $\alpha-$Ce obtained from the same calculation as shown in Fig.\ref{['fig:alpha_dos']} for k-integrated data.