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arXiv:2501.05825 · Physical review. B./Physical review. B

High-order strong-coupling expansion for x-ray absorption on a dynamically screened impurity

Eva Paprotzki, Martin Eckstein

Published Nov 21, 2025• 2 citations
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Abstract

Time-resolved x-ray absorption can reveal the dynamical screening of the local Coulomb interaction in strongly correlated photodoped materials. Here, we focus on the theoretical prediction of x-ray absorption in the presence of dynamical screening using the strong-coupling expansion, i.e., an expansion around the isolated absorption site in terms of the retarded interaction. The evaluation of higher-order diagrams is made numerically feasible by an approach based on the decomposition of the retarded interaction into complex exponentials. With this, we evaluate the strong-coupling series to third order on an electron-boson model of Holstein type. We demonstrate that in relevant coupling regimes, even low orders of the strong-coupling expansion can give a significant correction over the previously used lowest-order approximation.

DOI
10.1103/bl6z-14m9

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We extend the dynamical vertex approximation (DΓΓΓA), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-UUU DΓΓΓA", allows us to study strongly interacting electrons coupled to bosons including non-local spatial correlations on all length scales on top of the purely local ones captured by dynamical mean-field theory. We demonstrate the applicability of the method in the specific case of the coupling to a single dispersionless phononic mode, by studying the Hubbard-Holstein model on the square and cubic lattices, focusing on regimes of sizable Hubbard interactions where strong electronic correlations compete with phonon-mediated interactions. As illustrative examples, we consider the antiferromagnetic phase in the three-dimensional model and the d-wave superconductor in two dimensions, analyzing the effect of the electron-phonon coupling, including its frequency dependence, on both instabilities.
Optimized measurements for the susceptibility, self-energy, as well as three-leg and four-leg vertex functions are introduced for the continuous-time hybridization-expansion quantum Monte Carlo solver for the impurity model in the presence of a retarded interaction. The self-energy and vertex functions are computed from impurity averages which involve time integrals over the retarded interaction. They can be evaluated efficiently within the segment representation. These quantities are computed within dynamical mean-field theory in the presence of plasmonic screening. In the antiadiabatic regime, the self-energy is strongly renormalized but retains features of the low energy scale set by the screened interaction. An explicit expression for its high-frequency behavior is provided. Across the screening driven and interaction driven metal-insulator transitions, the vertex functions are found to exhibit similar structural changes, which are hence identified as generic features of the Mott transition.
Real-time impurity solvers enable the study of transport phenomena and the description of nonequilibrium lattice systems within the framework of dynamical mean-field theory (DMFT). They also provide direct access to the spectral functions of both equilibrium and nonequilibrium systems. A widely used approach is the self-consistent strong-coupling expansion, whose lowest-order implementation corresponds to the non-crossing approximation. Higher-order implementations, however, are computationally demanding because the number of diagram topologies grows factorially with expansion order, while the evaluation of self-energies and Green's functions requires increasingly high-dimensional integrations. Here, we demonstrate that the latter challenge can be mitigated by employing quantics tensor cross interpolation in a variable-separated framework. Compared with the previously used scale-separated approach, the new scheme yields substantially lower bond dimensions and capacitates self-consistent steady-state DMFT calculations up to fourth order. We illustrate its performance with representative results for both equilibrium and photo-doped systems. In addition, we analyze the convergence of the strong-coupling expansion in the challenging noninteracting limit by computing diagrams up to sixth order. At this order, the onset of the asymptotic regime of the strong-coupling expansion becomes apparent, which allows the application of extrapolation techniques.