Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study

Ultrafast irradiation of correlated electronic systems triggers complex dynamics involving quasi-particle excitations, doublons, charge carriers, and spin fluctuations. To describe these effects, we develop an efficient non-equilibrium approach, dubbed D-$GW$, that enables a self-consistent treatment of local correlations within dynamical mean-field theory (DMFT) and spatial charge and spin fluctuations, that are accounted for simultaneously within a diagrammatic framework. The method is formulated in the real-time domain and provides direct access to single- and two-particle momentum- and energy-dependent response functions without the need for analytical continuation, which is required in Matsubara frequency-based approaches. We apply the D-$GW$ method to investigate the dynamics of a photo-excited extended Hubbard model, the minimal system that simultaneously hosts strong charge and spin fluctuations. Focusing on the challenging parameter regime near the Mott transition, we demonstrate that correlated metals and narrow-gap Mott insulators undergo distinct thermalization processes involving complex energy transfer between single-particle and collective electronic excitations.

💡 Research Summary

This paper introduces a novel non‑equilibrium many‑body technique, called Dual‑GW (D‑GW), designed to treat both local electronic correlations and non‑local charge and spin fluctuations on equal footing in real time. Traditional non‑equilibrium dynamical mean‑field theory (DMFT) captures local self‑energies Σ(t,t′) accurately but neglects spatial collective modes, while GW‑EDMFT includes non‑local charge screening but omits spin fluctuations. The authors bridge this gap by starting from the equilibrium dual‑TRILEX (D‑TRILEX) formalism, which expands around a DMFT impurity reference and contains a three‑point vertex Λ(z₁,z₂,z₃). Because a full time‑dependent Λ would be computationally prohibitive, they approximate it by its instantaneous (short‑time) component. This simplification reduces the diagrammatic structure to a GW‑like one, yet retains the DMFT impurity self‑energy, thereby achieving a self‑consistent description of local and non‑local physics.

The method is formulated on the Keldysh contour (forward, backward, and imaginary branches) so that real‑time Green’s functions G(k,t,t′) and screened interactions W(q,t,t′) are obtained directly, without analytic continuation. The lattice action is split into a reference impurity part (with hybridization Δ) and a remainder. After Hubbard‑Stratonovich transformations, the remainder is expressed in terms of dual fermions f and bosons b, leading to an effective fermion‑boson action. The dual Green’s function ˜G and dual interaction ˜W are defined as differences between the DMFT quantities and the impurity solutions. The self‑energy and polarization are then computed from one‑loop diagrams involving ˜G, ˜W and the instantaneous vertex, yielding Σ̃(k,t,t′) and Π̃(q,t,t′). The full lattice self‑energy and screened interaction are reconstructed by adding back the impurity contributions.

To demonstrate the capability of D‑GW, the authors apply it to the half‑filled extended Hubbard model on a square lattice: H = –J∑⟨ij⟩c†i c j + U∑i n_{i↑} n_{i↓} + V∑⟨ij⟩ n_i n_j, subjected to an ultrashort electric field introduced via a Peierls substitution. The hopping J sets the energy scale (ℏ/J = 1 fs). Parameters are chosen near the Mott transition (U≈8J, V≈2J), allowing exploration of both the correlated metallic side (U≈6J) and the narrow‑gap Mott insulating side (U≈10J). A pump pulse with central frequency ω₀≈U/2, duration ≈5 fs, and moderate field strength excites the system.

Key findings are:

1. Correlated Metal – After the pulse, the electronic distribution rapidly thermalizes within ~30–40 fs. The dominant relaxation channel is the redistribution of kinetic energy into non‑local charge fluctuations, which screen the interaction efficiently. The system reaches a quasi‑thermal state characterized by a well‑defined effective temperature, and the momentum‑resolved spectral function shows a quick restoration of the quasiparticle peak.

2. Narrow‑Gap Mott Insulator – Photo‑excitation creates doublon–holon pairs, but their recombination is slow. The system remains in a long‑lived pre‑thermal plateau for several hundred femtoseconds. Importantly, the excess kinetic energy of high‑energy doublons is transferred to antiferromagnetic spin excitations (magnons) through an impact‑ionization‑like process. This manifests as a redistribution of spectral weight from high‑energy occupied states to lower energies and a simultaneous growth of spin‑fluctuation spectra. The spin channel thus acts as an energy sink, while charge screening remains weak.

3. Charge vs. Spin Screening – In the metallic regime, charge fluctuations dominate the dynamical screening, leading to a rapid reduction of the effective interaction. In the insulating regime, spin fluctuations become the primary channel for energy absorption, and the screened interaction retains a strong residual component, reflecting the persistence of the Mott gap.

4. Experimental Relevance – The calculated time‑dependent density of states and spin‑susceptibility can be directly compared with time‑resolved ARPES and pump‑probe magnetic spectroscopy. The predicted impact‑ionization mechanism suggests that even in the presence of strong antiferromagnetic correlations, high‑energy carriers can efficiently lose energy to magnons, a process observable as a transient softening of magnetic excitations.

Overall, D‑GW provides a computationally tractable yet quantitatively reliable framework for studying ultrafast phenomena in strongly correlated materials where both local Hubbard physics and long‑range collective modes are essential. The method scales favorably with the number of orbitals and can be extended to multi‑band systems, electron‑phonon coupling, and more complex pump protocols. The authors conclude that D‑GW opens a pathway toward realistic simulations of light‑driven phase transitions, hidden quantum states, and non‑thermal critical behavior in a broad class of quantum materials.