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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Improving the accuracy of the variational quantum eigensolver for molecular systems by the explicitly-correlated perturbative [2] R12 -correction

We provide an integration of the universal, perturbative explicitly correlated [2] R12 -correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. The proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in the VQE. This computation comes at a cost that scales as the sixth power of the number of electrons. Here, we explore the performance of the VQE + [2] R12 approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2] R12 . In particular the combination of MRA-PNOs with [2] R12 has turned out to be very promising – persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a complexity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Toward more accurate adiabatic connection approach for multireference wavefunctions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the “fixed-RDM” approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

All about the neutron from lattice QCD

I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between which matrix elements of operators are calculated. Both constructs are stochastic, so unfortunately one gets no intuitive picture or even qualitative understanding of what they look like, nevertheless they contain and display all the subtleties of the quantum field theory. Today, these simulations provide many quantities that are impacting phenomenology and experiments. I illustrate the methods and the steps in the analysis using, as examples, three observables: the isovector charges of the nucleon, the contribution of the quark’s intrinsic spin to the nucleon spin, and the pion-nucleon sigma term.

Gupta, Rajan (ORCID:0000000317843058)↗
DOE OSTI2023

Quantum information approach to the implementation of a neutron cavity

Abstract Using the quantum information model of dynamical diffraction we consider a neutron cavity composed of two perfect crystal silicon blades capable of containing the neutron wavefunction. We show that the internal confinement of the neutrons through Bragg diffraction can be modelled by a quantum random walk. Furthermore, we introduce a toolbox for modelling crystal imperfections such as surface roughness and defects. Good agreement is found between the simulation and the experimental implementation, where leakage beams are present, modelling of which is impractical with the conventional theory of dynamical diffraction. Analysis of the standing neutron waves is presented in regards to the crystal geometry and parameters; and the conditions required for well-defined bounces are derived. The presented results enable new approaches to studying the setups utilizing neutron confinement, such as the experiments to measure neutron magnetic and electric dipole moments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Shake loss intensities in x-ray photoelectron spectroscopy: Theory, experiment, and atomic composition accuracy for MgO and related compounds

The relative intensities of XPS core levels, scaled by their photoionization cross sections, are regularly used to determine sample atomic composition. Cross sections, however, give the intensity to all possible final states for the core ionizations, not just to the main peak. This includes all intrinsic satellite structure (shake states and, for open shell systems, the different ionic multiplets). In practice, for solids, this is usually experimentally impossible to determine accurately because such a satellite structure sits on the inelastically scattered electron background and cannot be easily separated. Therefore, usually, only the intensity of the main peak is used. This limits the ultimate possible accuracy of XPS composition determination. The purpose of the present paper is to examine the contributions that a theoretical analysis of losses of intensity can make to improve quantitation. For an MgO single crystal, we show that the correct stoichiometry of 1:1 can be recovered using the theoretical analysis of the experimental MgO peak ratio intensities. For materials with a sufficient bandgap for the XPS main peaks to be separated from the scattered background, the intensity of main peaks can often be accurately determined. Thus, if one uses theory to calculate that fraction of the total intensity lost from a main peak into all its satellite structure, the intensity of just main peaks could then be used to more accurately determine relative atom % composition. This work tests this approach using a single crystal MgO (50% Mg, 50% O) standard. Ab initio electronic structure theory of representative MgO clusters is used to determine Hartree–Fock wave functions for the ground state and final ionized states corresponding to the main Mg 2p and O1s XPS peaks of the oxide. The sudden approximation, SA, is used to determine the fractional losses from these main peaks to shake satellites, which is found to be greater for O1s than Mg2p. This results in predicted “apparent composition” for stoichiometric MgO of 55.2% Mg, 44.8% O instead of the true 50% Mg, 50% O. Equivalent theory for CaO results in a predicted apparent Ca value of 53.4%. Experimentally, using Mg2s or 2p intensity ratio to O1s, we find values between 52.2% and 56.0% Mg using two crystals and four different instrument electron pass energies. The average value of the measurements is 54.5% Mg when corrected for the presence of an adventitious carbon overlayer and slight surface hydroxide. Though this agreement with theory may be somewhat fortuitous, given the potential experimental errors, which are fully discussed, it is similar to that in our earlier study on LiF. We also present preliminary experimental data on Mg(OH) 2 and MgSO 4 , which show a similar trend of apparently higher than 50% Mg, but we have no theory values. We are not yet able to experimentally test for validation of the difference between apparent composition for MgO (55.2% Mg) and CaO (53.4% Ca), owing to significant carbonate formation at the surface of the single crystal CaO. Here, an important conclusion is that the theoretical determination of shake losses, obtained with ab initio wavefunctions and the SA, is likely to be a useful way to calibrate the accuracy and reliability of compositions obtained from XPS intensities and merits further study.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2023

Orbital dependent complications for close vs well-separated electrons in diradicals

We investigate two limits in open-shell diradical systems: O3, in which the interesting orbitals are in close proximity to one another, and (C21H13)2, where there is a significant spatial separation between the two orbitals. In accord with earlier calculations, we find that standard density-functional approximations do not predict the open-shell character for the former case but uniformly predict the open-shell character for the latter case. We trace the qualitatively incorrect behavior in O3 predicted by these standard density functional approximations to self-interaction error and use the Fermi–Löwdin-orbital-self-interaction-corrected formalism to determine accurate triplet, closed-shell singlet, and open-shell broken-spin-symmetry electronic configurations. Analysis of the resulting many-electron overlap matrices allows us to unambiguously show that the broken-spin-symmetry configurations do not participate in the representation of the Ms = 0 triplet states and allows us to reliably extract the singlet–triplet splitting in O3 by analyzing the energy as a function of Fermi-orbital-descriptor permutations. The results of these analyses predict the percentage of open-shell character in O3, which agrees well with conventional wavefunction-based methods. While these techniques are expected to be required in cases near the Coulson–Fischer point, we find that they will be less necessary in diradical systems with well-separated electrons, such as (C21H13)2. Results based on energies from self-interaction-corrected generalized gradient, local density, and Hartree–Fock approximations and experimental results are in generally good agreement for O3. These results help form the basis for deriving extended Heisenberg-like Hamiltonians that are needed for descriptions of molecular magnets when there are competing low-energy electronic configurations.

Chemistry↗
DOE OSTI2021

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗
DOE OSTI2024

Triplet‐Singlet Emission of d‐Block Metal Complexes Characterized by Spin‐Orbit Natural Transition Orbitals

Abstract Spin‐orbit natural transition orbital (SO‐NTO) methodology, recently developed in our group for complete and restricted active space (CAS/RAS) wavefunction calculations, is applied to analyze triplet‐to‐singlet emission in transition metal complexes. The lowest‐energy (longest‐wavelength) spin‐forbidden transition is studied for for [Ir(pbt)2(acac)] and [Re(CO)4(pbt)] and the complexes [W(CO)4(bpy)] and [Mo(CO)4(bpy)]. For the latter complexes, spin‐forbidden transitions from higher spin‐triplet levels are additionally analyzed. SO‐NTOs are compared with spin‐free NTOs for the transitions under consideration. The major assignment of a spin‐forbidden transition is obtained from the spin‐free NTO analysis, while the source of intensity of the electronic transition is revealed by the SO‐NTOs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree–Fock virtual orbitals by natural orbitals (NOs). Here, in this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller–Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al. J. Chem. Theory Comput. 17, 5509, (2021)]. Our implementation can manipulate complex or quaternion density matrices, thus allowing for the generation of both Kramers-restricted and Kramers-unrestricted MP2FNOs. Furthermore, NOs are re-expressed in the parent atomic orbital (AO) basis, allowing for generating coupled cluster singles and doubles NOs in the AO basis for further analysis. By investigating the truncation errors of MP2FNOs for both the correlation energy and molecular properties—electric field gradients at the nuclei, electric dipole and quadrupole moments for hydrogen halides HX (X = F–Ts), and parity-violating energy differences for H 2 Z 2 (Z = O–Se)—we find MP2FNOs accelerate the convergence of the correlation energy in a roughly uniform manner across the Periodic Table. It is possible to obtain reliable estimates for both energies and the molecular properties considered with virtual molecular orbital spaces truncated to about half the size of the full spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

First-principles computations of the Stark shift of a defect-bound exciton: The case of the T center in silicon

The T center in silicon has recently drawn a lot of attention for its potential in quantum information science. The sensitivity of the zero-phonon line (ZPL) to electrical field was recently investigated by a combination of different experimental methods but there are still few first principles studies on the Stark shift of the T center. Dealing with the defect-bound exciton nature of the excited state is particularly challenging using density functional theory because of the large spatial delocalization associated with the wavefunction. Here, in this work, we tackle this issue by performing a convergence study over the supercell size. We obtain an exciton binding energy of 28.5 meV, in good agreement with experimental results. We then calculate the Stark shift through the dipole moment change of the ZPL transition of the T center using the modern theory of polarization formalism and find a modest linear coefficient of Δ⁢𝜇=0.79⁢D along X and Δ⁢𝜇=0.03⁢𝐷 along Y. We discuss our results in light of the recent experimental measurements of the Stark shift. Our analysis suggests that bound-exciton defects could be particularly sensitive to local field effect as a result of their large spatial extent.

color centers↗
DOE OSTI2022

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Stability of superconducting strings

We investigate the stability of superconducting strings as bound states of strings and fermion zero modes at both the classical and quantum levels. The dynamics of these superconducting strings can result in a stable configuration, known as a vorton . We mainly focus on global strings, but the majority of the discussion can be applied to local strings. Using lattice simulations, we study the classical dynamics of superconducting strings and confirm that they relax to the vorton configuration through Nambu-Goldstone boson radiation, with no evidence of over-shooting that would destabilize the vorton. We explore the tunneling of fermion zero modes out of the strings. Both our classical analysis and quantum calculations yield consistent results: the maximum energy of the zero mode significantly exceeds the fermion mass, in contrast to previous literature. Additionally, we introduce a world-sheet formalism to evaluate the decay rate of zero modes into other particles, which constitute the dominant decay channel. We also identify additional processes that trigger zero-mode decay due to non-adiabatic changes of the string configuration. In these decay processes, the rates are suppressed by the curvature of string loops, with exponential suppression for large masses of the final states. We further study the scattering with light charged particles surrounding the string core produced by the zero-mode current and find that a wide zero-mode wavefunction can enhance vorton stability.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A = 3 ( e , e ' ) x B ≥ 1 cross-section ratios and the isospin structure of short-range correlations

We study the relation between measured high-x B , high-Q 2 , helium-3 to tritium, (e,e') inclusive-scattering cross-section ratios and the relative abundance of high-momentum neutron-proton (np) and proton-proton (pp) short-range correlated (SRC) nucleon pairs in three-body (A=3) nuclei. In this study, analysis of this data using a simple pair-counting cross-section model suggested a much smaller np/pp ratio than previously measured in heavier nuclei, questioning our understanding of A=3 nuclei and, by extension, all other nuclei. Here we examine this finding using spectral-function-based cross-section calculations, with both an ab initio A=3 spectral function and effective Generalized Contact Formalism (GCF) spectral functions using different nucleon-nucleon interaction models. The ab initio calculation agrees with the data, showing good understanding of the structure of A=3 nuclei. An 8% uncertainty on the simple pair-counting model, as implied by the difference between it and the ab initio calculation, gives a factor of 5 uncertainty in the extracted np/pp ratio. Thus we see no evidence for the claimed "unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3."

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

J/Psi Photoproduction Near Threshold With CLAS12

The structure of the proton is comprised of quarks and a sea of gluons. A mechanism that can extract the characteristics of the hidden-color correlations of the nuclear wavefunction is the production of charm near threshold. Due to the fact that momentum transfer is large near threshold in the production of J/ψ , all three valence quarks must act coherently to ex- change energy for the reaction to occur. Models have been developed to predict the nature of J/ψ photoproduction at these specific energies. These include production mechanisms with the two-gluon and three-gluon exchanges. The transferred momentum dependence of the differential cross sections are sensitive to the gluonic form factors, which describe the distribution of color charge in the proton. The CLAS12 detector is capable of measuring J/ψ photoproduction at the energy range close to the threshold. Work showcased in this dissertation encompasses the preparation of the CLAS12 experiments, including the optimization of tracking reconstruction through the study of the Torus magnetic field. In terms of software, contributions were made to the CLAS12 Event Builder, a key stage of reconstruction where event-by-event information is summarized for efficient data analysis. After the run periods were successfully completed, analysis of the RG-A data commenced and an analysis framework was developed to measure the differential and total cross sections of J/ψ photoproduction in Hall B.

Newton, Joseph↗
DOE OSTI2023

Controlling Molecular Structure and Spin with Multiconfigurational Quantum Chemistry (Final Technical Report)

For many first-row transition metal complexes, structure-property relationships can be obtained from high-level molecular geometry optimizations and subsequent electronic structure studies. The project funded under this award utilized newly implemented fully internally contracted (FIC) nuclear gradients for extended multi-state (XMS) complete active space second-order multireference perturbation theory (CASPT2) to explore geometry changes in first-row transition metal coordination complexes. At the start of the project, only one full geometry optimization using FIC-CASPT2 analytical gradients had been reported (J. Chem. Theory Comput., 2016, 12 (8), 3781), and many open-questions regarding the performance and achievable accuracy in applying such computations to larger complexes persisted. Key deliverables in the report include the implementation of the numerical Hessian and subsequent vibrational analysis in the BAGEL program package. This includes both full Hessian vibrational analysis (FHVA) and a partial Hessian vibrational analysis (PHVA). The latter of which allows us to reduce the significant cost of computing the vibrational frequencies in a large molecule by focusing on the modes of highest interest. The gradient code also proved useful in the development of an approach to improve the Hubbard-U correction by removing bias in predicting spin-splitting in Fe(II) complexes via plane-wave density functional theory (DFT). Finally, we showed for three families of complexes (spin-crossover (SCO) complexes, metallocorroles complexes, and those with metal-metal bonds) that CASPT2 can result in good molecular geometries and established best practices in undertaking this work. We are now using this approach in collaborative projects with experimental groups, which would not have been possible at the start of this project. A common theme also arose through this work that static and dynamic correlation must be recovered in a balanced way to yield quantitative results. By systematically varying how both effects were included, we were able to make key chemical insights. This work supported the training of two postdoctoral scholars, one graduate student, and one undergraduate student in applying high-level wavefunction based methods to challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Renormalization of states and quasiparticles in many-body downfolding

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.

Green-functions technique↗