Rydberg excited states of molecules pose a challenge for electronic structure calculations because of their highly diffuse electron distribution. Even large and elaborate atomic basis sets tend to underrepresent the long-range tail, overly confining the Rydberg state. An approach is presented here where the molecular orbitals are variationally optimized for the excited state using a plane wave basis set in a Hartree-Fock calculation, followed by a configuration interaction calculation. The use of excited state optimized orbitals greatly enhances the convergence of the many-body calculation, as illustrated by a full configuration interaction calculation of the 2s Rydberg state of H2. A neural-network-based selective configuration interaction approach is then applied to calculations of 3s and 3p states of H2O and NH3. The obtained values of excitation energy are in close agreement with experimental measurements as well as previous many-body calculations where sufficiently diffuse atomic basis sets were used. Calculations using atomic basis sets lacking extra diffuse functions, such as aug-cc-pVTZ, give significantly higher estimates due to confinement of the Rydberg states.

The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of states upon cooling. We show how these phenomena are originating in the three-band Emery model by performing cutting-edge dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound our results demonstrate the formation of a pseudogap due to short-ranged commensurate antiferromagnetic fluctuations. At larger doping values, progressively, incommensurate correlations and a metallic regime appear. Our results are in qualitative agreement with the normal state of cuprates, and, hence, represent a crucial step towards the uniform description of their phase diagrams within a single theoretical framework.

We propose three transition-metal adatom systems on SiC surfaces as a versatile platform to realize massless Dirac fermions and flat bands with strong electronic correlations. Using density functional theory combined with the constrained random phase approximation and dynamical mean-field theory, we investigate the electronic properties of Ti, V, and Cr adatoms. The triangular surface lattices exhibit narrow bandwidths and effective two-band Hubbard models near the Fermi level, originating from partially filled adatom d orbitals. For the undoped systems our calculations reveal two distinct Mott insulating ground states. While the V lattice is a paramagnetic textbook case with large local moments, the Cr lattice, in contrast, is on the edge of a phase transition toward a flat-band Fermi liquid. The Ti lattice realizes a heavy Dirac semimetal at zero doping.

The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter.

We investigate dynamical mean-field calculations of the three-band Emery model at the one- and two-particle level for material-realistic parameters of high-T_c superconductors. Our study shows that even within dynamical mean-field theory, which accounts solely for temporal fluctuations, the intrinsic multi-orbital nature of the Emery model introduces effective non-local correlations. These correlations lead to a non-Curie-like temperature dependence of the magnetic susceptibility, consistent with nuclear magnetic resonance experiments in the pseudogap regime. By analyzing the temperature dependence of the uniform static spin susceptibility obtained by single-site and cluster dynamical mean-field theory, we find indications of emerging oxygen-copper singlet fluctuations, explicitly captured by the model. Despite correctly describing the hallmark of the pseudogap at the two-particle level, such as the drop in the Knight shift of nuclear magnetic resonance, dynamical mean-field theory fails to capture the spectral properties of the pseudogap.

The family of infinite-layer nickelates promises important insights into the mechanism of unconventional superconductivity. Since superconductivity has so far only been observed in epitaxial thin films, heteroepitaxy with the substrate or a capping layer possibly plays an important role. Here, we use soft x-ray spectroscopy to investigate superlattices as a potential approach for a targeted material design of high-temperature superconductors. We observe modulations in valence state and oxygen coordination in topotactically reduced artificial superlattices with repeating interfaces between nickelate layers and layers of materials commonly used as substrates and capping layers. Our results show that depending on the interlayer material metallic conductivity akin to the parent infinite-layer compounds is achieved. Depth-resolved electronic structure measured by resonant x-ray reflectivity reveals a reconstructed ligand field and valence state at the interface, which is confined to one or two unit cells. The central layers are predominantly monovalent nickel, but linear dichroism analysis reveals considerable disorder in the oxygen removal sites. We observe a quantitative correlation of this disorder with the interlayer material that is important for future modeling and design strategies.

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze fermionic quantum systems using the formalism of second quantization. SOLAX provides a modular framework for constructing and manipulating basis sets, quantum states, and operators, facilitating the simulation of electronic structures and determining many-body quantum states in finite-size Hilbert spaces. The library integrates machine learning capabilities to mitigate the exponential growth of Hilbert space dimensions in large quantum clusters. The core low-level functionalities are implemented using the recently developed Python library JAX. Demonstrated through its application to the Single Impurity Anderson Model, SOLAX offers a flexible and powerful tool for researchers addressing the challenges of many-body quantum systems across a broad spectrum of fields, including atomic physics, quantum chemistry, and condensed matter physics.

Selective configuration interaction methods approximate correlated molecular ground- and excited states by considering only the most relevant Slater determinants in the expansion. While a recently proposed neural-network-assisted approach efficiently identifies such determinants, the procedure typically relies on canonical Hartree-Fock orbitals, which are optimized only at the mean-field level. Here we assess approximate natural orbitals - eigenfunctions of the one-particle density matrix computed from intermediate many-body eigenstates - as an alternative. Across our benchmarks for H$_2$O, NH$_3$, CO, and C$_3$H$_8$ we see a consistent reduction in the required determinants for a given accuracy of the computed correlation energy compared to full configuration interaction calculations. Our results confirm that even approximate natural orbitals constitute a simple yet powerful strategy to enhance the efficiency of neural-network-assisted configuration interaction calculations.

By combining Hartree-Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method's performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N2 molecule is compared with published full CI calculations that included nearly 1010 Slater determinants, and the results are reproduced with only 4 × 105 determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method's high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.

Delafossites, composed of noble metal (A+) and strongly correlated sublayers (BO2-), form natural superlattices with highly anisotropic properties. These properties hold significant promise for various applications, but their exploitation hinges on the successful growth of high-quality thin films on suitable substrates. Unfortunately, the unique lattice geometry of delafossites presents a significant challenge to thin-film fabrication. Different delafossites grow differently, even when deposited on the same substrate, ranging from successful epitaxy to complete growth suppression. These variations often lack a clear correlation to obvious causes like lattice mismatch. Unidentified stabilization mechanisms appear to enable growth in certain cases, allowing these materials to form stable thin films or act as buffer layers for subsequent delafossite growth. This study employs advanced scanning transmission electron microscopy techniques to investigate the nucleation mechanism underlying the stable growth of PdCoO2 films on Al2O3 and LaAlO3 substrates grown via molecular-beam epitaxy. Our findings reveal the presence of a secondary phase within the substrate surface that stabilizes the films. This mechanism deviates from the conventional understanding of strain relief mechanisms at oxide heterostructure interfaces and differs significantly from those observed for Cu-based delafossites.

A deep-learning approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground-state wavefunction. We benchmark our results against established methods and investigate the efficiency of our approach as compared to other basis truncation schemes. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.

We formulate a quantum embedding algorithm in real-space for the simultaneous theoretical treatment of nonlocal electronic correlations and disorder, the coherent cellular dynamical mean-field theory (C-CDMFT). This algorithm combines the molecular coherent potential approximation (CPA) with the cellular dynamical mean-field theory. After a pedagogical review of quantum embedding theories for disordered and interacting electron systems, and a detailed discussion of its work flow, we present first results from C-CDMFT for the half-filled two-dimensional Anderson–Hubbard model on a square lattice: (i) the analysis of its Mott metal–insulator transition as a function of disorder strength, and (ii) the impact of different types of disorder on its magnetic phase diagram. For the latter, by means of a ‘disorder diagnostics’, we are able to precisely identify the contributions of different disorder configurations to the system’s magnetic response.

The discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ at pressures above 14 GPa has spurred extensive research efforts. Yet, fundamental aspects of the superconducting phase, including the possibility of a filamentary character, are currently subjects of controversial debates. Conversely, a crystal structure with NiO$_6$ octahedral bilayers stacked along the $c$-axis direction was consistently posited in initial studies on La$_3$Ni$_2$O$_7$. Here we reassess this structure in optical floating zone-grown La$_3$Ni$_2$O$_7$ single crystals that show signs of filamentary superconductivity. Employing scanning transmission electron microscopy and single-crystal x-ray diffraction under high pressures, we observe multiple crystallographic phases in these crystals, with the majority phase exhibiting alternating monolayers and trilayers of NiO$_6$ octahedra, signifying a profound deviation from the previously suggested bilayer structure. Using density functional theory, we disentangle the individual contributions of the monolayer and trilayer structural units to the electronic band structure of La$_3$Ni$_2$O$_7$, providing a firm basis for advanced theoretical modeling and future evaluations of the potential of the monolayer-trilayer structure for hosting superconductivity.

The Mott insulator Ca2RuO4 exhibits an insulator-to-metal transition induced by d.c. current. Despite the thorough examination of the structural changes associated with this transition, a comprehensive knowledge of the response of electronic degrees of freedom is still lacking. Here we demonstrate current-induced modifications of the electronic states of Ca2RuO4. Angle-resolved photoemission spectroscopy in conjunction with four-probe electrical transport (transport-ARPES) measurements reveal a clear reduction of the Mott gap and a modification in the dispersion of the Ru bands. Based on a free-energy analysis, we show that the current-induced phase is electronically distinct from the high-temperature zero-current metallic phase. Our results highlight strong interplay of lattice- and orbital-dependent electronic responses in the current-driven insulator-to-metal transition. Ca2RuO4 is a Mott insulator that becomes a metal when a current is passed through it. Now, the changes in its electronic structure are revealed as this transition takes place.

The recently proposed center-focused post-processing procedure [Phys. Rev. Res. 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to 8×8 in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the 4×4 cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.

The topological classification of electronic band structures is based on symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In parallel, topological field theory has opened the doors to the formulation and characterization of non-trivial phases of matter driven by strong electron-electron interaction. Even though important examples of topological Mott insulators have been constructed, the relevance of the underlying non-interacting band topology to the physics of the Mott phase has remained unexplored. Here, we show that the momentum structure of the Green's function zeros defining the “Luttinger surface" provides a topological characterization of the Mott phase related, in the simplest description, to the one of the single-particle electronic dispersion. Considerations on the zeros lead to the prediction of new phenomena: a topological Mott insulator with an inverted gap for the bulk zeros must possess gapless zeros at the boundary, which behave as a form of “topological antimatter” annihilating conventional edge states. Placing band and Mott topological insulators in contact produces distinctive observable signatures at the interface, revealing the otherwise spectroscopically elusive Green's function zeros.

We investigated the electronic structure of the enigmatic CeRh_3B_2 using resonant inelastic scattering and x-ray absorption spectroscopy in combination with ab initio density functional calculations. We find that the Rh 4d states are irrelevant for the high-temperature ferromagnetism and the Kondo effect. We also find that the Ce 4f crystal-field strength is too small to explain the strong reduction of the Ce magnetic moment. The data reveal instead the presence of two different active Ce 4f orbitals, with each coupling selectively to different bands in CeRh_3B_2. The inter-site hybridization of the |J=5/2,Jz=+/-1/2> crystal-field state and Ce 5d band combined with the intra-site Ce 4f-5d exchange creates the strong ferromagnetism, while hybridization between the |J=5/2,Jz=+/-5/2> and the B sp in the ab-plane contributes to the Kondo interaction which causes the moment reduction. This orbital selective coupling explains the unique and seemingly contradictory properties of CeRh_3B_2.

The unconventional superconductor Sr_2RuO_4 has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru L_3-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr_2RuO_4 over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr_2RuO_4 and provide key information for the understanding of its unconventional superconductivity.

The Mott insulator Ca_2RuO_4 exhibits a rare insulator-to-metal transition (IMT) induced by DC current. While structural changes associated with this transition have been tracked by neutron diffraction, Raman scattering, and x-ray spectroscopy, work on elucidating the response of the electronic degrees of freedom is still in progress. Here we unveil the current-induced modifications of the electronic states of Ca_2RuO_4 by employing angle-resolved photoemission spectroscopy (ARPES) in conjunction with four-probe transport. Two main effects emerge: a clear reduction of the Mott gap and a modification in the dispersion of the Ru-bands. The changes in dispersion occur exclusively along the XM high-symmetry direction, parallel to the b-axis where the greatest in-plane lattice change occurs. These experimental observations, together with dynamical mean-field theory (DMFT) calculations simulated from the current-induced structural distortions, indicate the intimate interplay of lattice and orbital-dependent electronic response in the current-driven IMT. Furthermore, based on a free energy analysis, we demonstrate that the current-induced phase, albeit thermodynamically equivalent, is electronically distinct from the high-temperature zero-current metallic phase. Our results provide insight into the elusive nature of the current-induced IMT of Ca_2RuO_4 and advance the challenging, yet powerful, technique of transport-ARPES.