We present a unified many-body perturbation theory for open quantum systems that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce a diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations and identify the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full Kadanoff-Baym equations retain their closed-form structure and can be efficiently used to simulate relaxation and decoherence dynamics. The impact of dissipation-induced correlations is illustrated in the driven Haldane model, where quasiparticles exhibit nontrivial stabilization and acquire lifetimes that far exceed those of the bare system. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the stochastic cluster expansion (SCE) framework previously developed for ground-state correlation energies, we extend the formalism to excitation gaps by expressing energy differences directly as a hierarchy of orbital-space cluster contributions. In this formulation, excitation energies are reconstructed from reduced-rank calculations involving a minimal frontier chemical subspace (FCS), treated exactly, together with stochastic sampling of the remaining orbital environment. This approach greatly diminishes the dependence on large or chemically preselected active spaces. We demonstrate the method on charge-transfer complexes and polyacenes, where accurate singlet-triplet gaps are obtained that agree with full-system results. The method converges with low-order cluster terms and provides a systematically improvable framework for excited states in correlated systems.

Electronic spectra provide direct insight into the excitations and correlations of condensed matter systems. Their description requires electron correlations beyond mean field. In equilibrium, the GW approximation has become the method of choice for many materials. Extending this approximation to nonequilibrium, however, is challenging. Full two-time GW simulations within the nonequilibrium Green's functions approach scale at least cubically with propagation time, whereas improved scaling schemes such as time-local (adiabatic) approximations or the generalized Kadanoff–Baym ansatz usually retain only mean-field character in the spectra. The recently introduced real-time Dyson expansion recovers dynamical correlations in the spectrum at time-linear cost, but has so far been restricted to the second-order Born approximation with mean-field reference propagators. Here we formulate and implement the RT-DE for the nonequilibrium GW self-energy with reference propagators of general form whose off-diagonal evolution is time local. In particular, we assess Hartree–Fock propagators, propagators with statically screened exchange with nonequilibrium screening, and a correlated propagator based on the Hartree–Fock GKBA. Benchmarks against exact diagonalization for a driven two-band lattice model with long-range interactions show that the mean-field and statically screened references yield the most accurate spectra, including satellite structures absent at mean-field level, whereas the GKBA-based approach best captures scattering-induced occupation dynamics, but artificially broadens and splits spectral peaks. When applied to large systems that are beyond the reach of exact methods, the scheme resolves the excitonic replica of the valence band and satellites identified as exciton shake-up, as well as their reshaping with increasing excitation density.

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established non-equilibrium Green's function approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal Green's functions, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz (GKBA), and exact diagonalization for small systems using second order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the Green's functions, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich non-equilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and bandgap renormalization, which are largely washed out in self-consistent approaches, yet are present in the exact solutions. Our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

Excitons in the weakly interacting regime can be well-described by many-body perturbation theories such as the Bethe-Salpeter equation formalism. However, for materials such as transition metal dichalcogenides moiré heterostructures under strong illumination, with the emergence of dense excitonic states, the strong correlation and entanglement between electrons and holes may cause the many-body perturbation method to fail, and excitons may not be treated in the bosonic picture, but exhibit fermionic behaviors. In our work, we investigate the phase space where excitons, and the electrons and holes which constitute them, are weakly or strongly entangled, as well as their binding for different interaction profiles and the degree of localization of the electrons and holes. We corroborate the validity of using many-body perturbation theory in the exciton with interactions. Our work provides a general way to analyze the correlation and entanglement of multi-particle excitations in many-body systems, and gives a more comprehensive understanding of different phases for exciton entanglement and interactions in 1D systems.

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the stochastic cluster expansion (SCE) framework previously developed for ground-state correlation energies, we extend the formalism to excitation gaps by expressing energy differences directly as a hierarchy of orbital-space cluster contributions. In this formulation, excitation energies are reconstructed from reduced-rank calculations involving a minimal frontier chemical subspace (FCS), treated exactly, together with stochastic sampling of the remaining orbital environment. This approach eliminates the need for large or chemically preselected active spaces. We demonstrate the method on charge-transfer complexes and polyacenes, where accurate singlet-triplet gaps are obtained that agree with full-system results. The method converges with low-order cluster terms and provides a systematically improvable framework for excited states in correlated systems.

Ab initio downfolding describes the electronic structure of materials within a low-energy subspace, often around the Fermi level. Typically starting from mean-field calculations, this framework allows for the calculation of one-and two-electron interactions, and the parametrization of a many-body Hamiltonian representing the active space of interest. The subsequent solution of such Hamiltonians can provide insights into the physics of strongly correlated materials. While phonons can substantially screen electron-electron interactions, electron-phonon coupling has been commonly ignored within ab initio downfolding, and when considered, this is done only for short-range coupling. Here we propose a theory of ab initio downfolding that accounts for short-and long-range electron-phonon coupling on equal footing. Our practical computational implementation is readily compatible with current downfolding approaches. We apply our approach to polar materials MgO and GeTe, and we reveal the importance of both short-range and long-range electron-phonon coupling in determining the magnitude of electron-electron interactions. Our results show that in the static limit, phonons reduce the on-site repulsion between electrons by 40% for MgO and by 79% for GeTe. Our framework also predicts that overall attractive nearest-neighbor interactions arise between electrons in GeTe, consistent with superconductivity in this material.

Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as the full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding and embedding approaches mitigate this cost but typically require prior selection of a correlated subspace, which can be difficult to determine in heterogeneous or extended systems. Here, we introduce a stochastic cluster expansion framework for efficiently recovering the total correlation energy of large systems with near-DMRG accuracy and without the need to select an active space a priori. By combining correlation contributions from randomly sampled environment orbitals with an exactly treated subspace of interest, the method reproduces total energies for nonreacting and reactive systems while drastically reducing computational cost. The approach also provides a quantitative diagnostic for molecule-solvent correlation, guiding principled embedding decisions. This framework enables systematically improvable many-body calculations in extended systems, opening the door to high-accuracy studies of chemical processes in condensed phase environments.

Topological materials have recently been proposed as a new class of catalysts, where robust surface states near the Fermi level are expected to influence adsorption and reactivity. In this Letter, using first-principles calculations, we systematically investigate molecular adsorption on bismuth (Bi) slabs across a wide range of adsorbates, spanning both trivial and topological electronic regimes. We find that open-shell adsorbates strongly hybridize with both topological and trivial surface states near the Fermi energy. Although adsorption is primarily governed by conventional chemical bonding, we quantitatively assess how surface states modulate binding energetics by comparing slabs (with surface states) to a monolayer. The COHP analysis further confirms that surface-state hybridization strongly reshapes the bonding and antibonding contributions near the Fermi level, thereby modulating the adsorption energetics. This framework also qualitatively accounts for the distinct catalytic performance between bulk-like slabs and monolayer Bi. Overall, topological character appears to play a more indirect role, while a surface-state-centric perspective may provide a useful framework for understanding catalytic behavior.

Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green's function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. In this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green's function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.

The DNA binding properties of methylene blue (MB) have been well characterized, but analysis of the DNA binding behavior of the reduced form, leucomethylene blue (LMB), has been minimal. We demonstrate here, via modeling and X-ray crystallography, that LMB is significantly bent into a "butterfly" conformation with an angle of ∼150 ° at the central sulfur and nitrogen atoms. Binding studies with single- and double-stranded DNA constructs using isothermal titration calorimetry, nuclear magnetic resonance spectroscopy, UV-vis absorbance spectroscopy, and fluorescence confirm binding by MB and show essentially no binding by LMB. As MB redox chemistry has become an integral component in many electrochemical DNA aptamer-based (E-AB) applications, better understanding of the presence and impact of this conformational change in LMB will inform future developments of this exciting biosensor class.

Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime.

Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely, the real-time Dyson expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven dynamically correlated systems and utilize these methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range densitydensity Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's band structure and a time-evolving band-gap renormalization (with a reduction by up to 8.4%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.

We extend the stochastic GW (sGW) formalism to fully spin-polarized systems, encompassing both collinear and noncollinear spin configurations. For noncollinear systems, where Kohn-Sham states are complex two-component spinors, we develop a complex-valued stochastic basis that preserves the real-valued external stochastic charge applied at time zero. This basis enables an unbiased evaluation of the random-phase approximation (RPA) screened interaction for spinors. Through error analysis and tests on real materials, we show that the performance of collinear sGW retains the same time complexity as the spin-unpolarized sGW. The noncollinear sGW incurs a computational cost two to three times higher than the spin-unpolarized version, while preserving linear scaling with low multiplicity. By unifying collinear and noncollinear treatments within a single scalable framework, our work paves the way for routine many-body predictions in large scale magnetic and spin-orbit-coupled material systems.

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Superconductivity in doped SrTiO_3 was discovered in 1964, the first superconducting transition observed in a doped semiconductor. However, the mechanism of electron pairing in SrTiO_3 remains a subject of debate. By developing a theoretical framework to incorporate dynamical lattice screening in the electronic Coulomb interactions of semiconductors and insulators, we demonstrate analytically that linear long-range coupling of electrons to multiple longitudinal optical phonons, described by a generalized Fröhlich mechanism, can result in superconductivity in SrTiO_3. Moreover, by combining our theory with first-principles calculations, we reveal an additional attractive interaction between electrons in SrTiO_3 due to the deformation potential mechanism, arising from the mixed ionic-covalent character of the Ti-O bond. Our results may have implications for the emergence of phonon-mediated electron attraction and superconductivity in a broad range of materials.

Chemical recycling of post-consumer plastics is an emerging area of study to decrease plastic waste and the use of virgin petrochemical feedstocks. Widespread application of chemical recycling processes has thus far been hindered, in part, due to a lack of fundamental understanding of the kinetics and mechanisms that govern complex depolymerization reactions. Here, we employ shrinking core models (SCMs) to quantitatively describe the kinetics of chemical recycling of a model polyurethane foam (M-PUF), the 6th-most produced polymer, via acidolysis with dicarboxylic acids (DCAs) to produce a recycled polyol (repolyol). Previous experimental analyses measured the rate of solid M-PUF decomposition by DCAs to produce liquid polyol and gaseous CO2 with 1 s time resolution. Here, single-component SCMs are demonstrated to effectively model experimental CO2 evolution measurements, which is concomitant with repolyol release, during M-PUF acidolysis with four different DCA substrates. A combined-resistance model is used to validate the results of the single-component models. The phase of transport of the DCA is observed to be the best descriptor of the rate-controlling regime. The rate of M-PUF acidolysis with DCAs that exist as liquids at reaction temperature are shown to be well described by reaction-controlled SCMs. Alternatively, the product formation rates with DCAs that are solid and thus transport via vaporization are best described by film-diffusion controlled SCMs. These results provide quantitative models that can aid in the development and scaleup of a circular plastic chemical recycling processes for polyurethane foams.

Subsurface oxygen in oxide-derived copper catalysts significantly influences CO2 activation. However, its effect on the molecular charging process, the key to forming the CO2δ- intermediate, remains poorly understood. We employ many-body perturbation theory to investigate the impact of the structural factors induced by the subsurface oxygen on the charged activation of CO2. By computing the molecular single-particle state energy of the electron-accepting orbital on the Cu (111) surface, we examined how this molecular quasi-particle (QP) energy changes with the varying vicinity of adsorption and multiple-subsurface oxygen configuration. We demonstrate that subsurface oxygen impairs CO2 charging, with its presence and coverage being influential factors. However, we remark that density functional theory calculations do not predict such an excitation energy discrepancy induced by subsurface oxygen. The nonlocal potential proves to be substantial for accurate excitation energy predictions yet is not sensitive to minor atomic structural changes. More importantly, state delocalization and hybridization are critical for determining QP energy. These insights are enlightening for designing atomic architectures to optimize catalytic performance on modified surfaces.

Molecules often adopt multiple conformations with distinct energies and reactivities, making it essential to characterize their conformational free energy landscape to understand their reactivity. Traditionally, computational studies identify stable molecular configurations using direct energy minimization with density functional theory (DFT), which effectively locates local minima. However, this approach does not fully capture the conformational landscape, particularly in the condensed phase where intermolecular interactions are playing a significant role. Here, we address this limitation by employing ab initio molecular dynamics (AIMD) to simulate the conformers of three dicarboxylic acids (DCAs), in both vapor and condensed phases. Our findings show that while direct energy minimization predicts the predominant conformer for fumaric acid (FA), AIMD is necessary to account for complex intermolecular interactions that stabilize additional conformers in succinic acid (SA) and maleic acid (MA). Specifically, AIMD reveals conformers that direct energy minimization does not predict to be thermally accessible but are stabilized by condensed-phase interactions. Additionally, we demonstrate a direct correlation between the density of the SA environment and the probability of forming external hydrogen bonds, which affects the conformational distribution. Finally, we demonstrate that these conformational distributions can serve as predictors for reactivity in an industrially relevant polyurethane acidolysis reaction.

The use of machine learning (ML) to refine low-level theoretical calculations to achieve higher accuracy is a promising and actively evolving approach known as Δ-ML. The density matrix renormalization group (DMRG) is a powerful variational approach widely used for studying strongly correlated quantum systems. High computational efficiency can be achieved without compromising accuracy. Here, we demonstrate the potential of a simple ML model to significantly enhance the performance of the quantum chemical DMRG method.