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Conflicting theoretical scenarios for infinite-layer nickelate superconductors have been hotly debated, particularly regarding whether {only} a single Ni-3$d_{x^2-y^2}$ band is relevant at low energies besides electron pockets or whether multi-orbital physics including Ni-3$d_{z^2}$ is instead essential. The first scenario has emerged from density-functional theory plus dynamical mean-field theory (DFT+DMFT) calculations. Comparing the previous DFT+DMFT spectra to recent angular-resolved photoemission spectroscopy (ARPES) experiments, we find excellent agreement for both the Fermi surface and the strongly renormalized quasi-particle bands, supporting the first scenario. Our key findings further suggest that the "waterfalls" observed in ARPES might emerge from the quasi-particle--to--Hubbard-band crossover, and that additional spectral weight close to the $A$-pocket likely originates from the Ni-3$d_{xy}$ orbital., Comment: 8 pages, 4 figures

Waterfalls are anomalies in the angle-resolved photoemission spectrum where the energy-momentum dispersion is almost vertical, and the spectrum strongly smeared out. These anomalies are observed at relatively high energies, among others, in superconducting cuprates and nickelates. The prevalent understanding is that they originate from the coupling to some boson, with spin fluctuations and phonons being the usual suspects. Here, we show that waterfalls occur naturally in the process where a Hubbard band develops and splits off from the quasiparticle band. Our results for the Hubbard model with $\textit{ab initio}$ determined parameters well agree with waterfalls in cuprates and nickelates., Comment: 7 pages, 4 figures, 1 mp4 file

We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the crossing symmetry, the Fierz decoupling ambiguity of the Hubbard interaction is resolved exactly. Our benchmarks for the half-filled Hubbard model on the square lattice are in very good agreement with numerically exact diagrammatic Monte Carlo simulations., Comment: 16 pages, 14 figures

Experimental studies have found unusual transport properties in Ce$_3$Bi$_4$Pd$_3$ which are potentially a consequence of the interplay between band-structure topology and electronic correlations. Based on these measurements, the existence of Weyl points in strongly renormalized, flat quasiparticle bands has been postulated. However, so far, there has been neither a direct spectroscopic observation of these, nor a calculation from first principles that would confirm their existence close to the Fermi energy. Here, we present density functional theory (DFT) and dynamical mean field theory (DMFT) calculations and study the low-energy excitations and their topological properties. We find that the Kondo effect promotes two out of the six angular momentum $J=5/2$ states, with the other four pushed to higher energies. Further, we find Weyl nodes close to the Fermi energy as previously suggested for explaining the observed giant spontaneous Hall effect in Ce$_3$Bi$_4$Pd$_3$, as well as nodal lines.

Thermoelectric (TE) materials are useful for applications such as waste heat harvesting or efficient and targeted cooling. While various strategies towards superior thermoelectrics through a reduction of the lattice thermal conductivity have been developed, a path to enhance the power factor is pressing. Here, we report large power factors up to 5 mW m$^{-1}$ K$^{-2}$ at room temperature in the kagome metal Ni$_3$In$_{1-x}$Sn$_x$. This system is predicted to feature almost dispersionless flat bands in conjunction with highly dispersive Dirac-like bands in its electronic structure around the Fermi energy $E_\text{F}$ [L. Ye et al., Nature Physics 1-5 (2024)]. Within this study, we experimentally and theoretically showcase that tuning this flat band precisely below $E_\text{F}$ by chemical doping $x$ boosts the Seebeck coefficient and power factor, as highly mobile charge carriers scatter into the flat-band states. Our work demonstrates the prospect of engineering extremely flat and highly dispersive bands towards the Fermi energy in kagome metals and introduces topological flat bands as a novel tuning knob for thermoelectrics.

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG.Due to the overcompleteness, we achieve only qualitative agreement., Comment: 9 pages, 4 figures

Correlated electron systems may give rise to multiple effective interactions whose combined impact on quasiparticle properties can be difficult to disentangle. We introduce an unambiguous decomposition of the electronic self-energy which allows us to quantify the contributions of various effective interactions simultaneously. We use this tool to revisit the hole-doped Hubbard model within the dynamical cluster approximation, where commonly spin fluctuations are considered to be the origin of the pseudogap. While our fluctuation decomposition confirms that spin fluctuations indeed suppress antinodal electronic spectral weight, we show that they alone can not capture the pseudogap self-energy quantitatively. Nonlocal multi-boson Feynman diagrams yield substantial contributions and are needed for a quantitative description of the pseudogap., Comment: 5 pages, 4 figures

We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable to drive the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs") as well as of the opening of a pseudogap at hole- and electron-doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc., Comment: 6 pages, 4 figures, suppl. mat

Strongly correlated electron systems are challenging to calculate, and entanglement in such systems is not widely analyzed. We present an approach that can be used as a post-processing step for calculating the two-site reduced density matrix and from it entanglement measures such as the mutual information and entanglement negativity. Input is only the one- and two-particle Green's function which is the output of numerous many-body methods. As an illustration, we present results for a toy model, the Hubbard model on a $2\times2$ cluster and a $6$ site ring., Comment: 19 pages, 15 figures

Infinite-layer nickelates show high-temperature superconductivity, and the experimental phase diagram agrees well with the one simulated within the dynamical vertex approximation (D$\Gamma$A). Here, we compare the spin-fluctuation spectrum behind these calculations to resonant inelastic X-ray scattering experiments. The overall agreement is good. This independent cross-validation of the strength of spin fluctuations strongly supports the scenario, advanced by D$\Gamma$A, that spin-fluctuations are the mediator of the superconductivity observed in nickelates., Comment: 13 pages, 8 figures

High-temperature unconventional superconductivity quite generically emerges from doping a strongly correlated parent compound, often (close to) an antiferromagnetic insulator. The recently developed dynamical vertex approximation is a state-of-the-art technique that has quantitatively predicted the superconducting dome of nickelates. Here, we apply it to study the effect of pressure in the infinite-layer nickelate Sr$_x$Pr$_ {1-x}$NiO$_2$. We reproduce the increase of the critical temperature ($T_c$) under pressure found in experiment up to 12 GPa. According to our results, $T_c$ can be further increased with higher pressures. Even without Sr-doping the parent compound, PrNiO$_2$, will become a high-temperature superconductor thanks to a strongly enhanced self-doping of the \nidxsqysq{} orbital under pressure. With a maximal \Tc{} of 100\,K around 100\,GPa, nickelate superconductors can reach that of the best cuprates., Comment: Main text: 6 pages, 4 figures. Supplementary information: 18 pages, 16 figures

Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an $\textit{ab initio}$ derived two-band model of the Cu $e_g$ orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin-singlet $d$-wave superconductivity at $T_{\mathrm{c}}\geq300$ K if the system is put close enough to a magnetic instability., Comment: 14 pages, 3 figures; revised submission to SciPost Physics

We briefly review the status quo of research on the putative superconductor Pb$_9$Cu(PO$_4$)$_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from substituting Pb by Cu and thus differs from LK-99) is required to make it metallic and potentially superconducting., Comment: 7 figures, 9 pages, 2 tables. Version 2 is the same as version 1 except for additional DMFT and DFT+U results in Secs. IV and V

A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf 33}, 61 (2023)] provides some experimental indications that Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with $x$ -- very similar to experiment. The DFT electronic structure shows Cu$^{2+}$ in a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This puts Pb$_{9}$Cu(PO$_4$)$_6$O in an ultra-correlated regime and suggests that, without doping, it is a Mott or charge transfer insulator. If doped such an electronic structure might support flat-band superconductivity or an correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results., Comment: 10 pages, 7 figures and 4 tables including supplementary materials

Oxygen vacancies in the perovskite insulator SrTiO$_3$ free electrons that couple with other physical degrees of freedom such as lattice, orbital, and spin. This leads to the emergence of exotic quantum states such as superconductivity and unusual ferromagnetism. We perform density-functional theory and dynamical mean-field theory calculations and demonstrate that the orientation and ordering of the TiO$_5$ pentahedra plays a crucial role. Specifically, for vacancy-rich SrTiO$_{3-\delta}$ ($\delta\sim$0.5), we find a chiral ordering of the TiO$_5$ pentahedra in a sixfold superlattice. This chiral structure is accompanied by a chiral magnetic state with a net moment in the (111) direction at room temperature, which can explain several experimental observations., Comment: 10 pages, 8 figures including supplementary materials

The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger--Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green's functions potentially leading to a classification of these in terms of their (ir)reducible components., Comment: Submission to SciPost

A recent experiment [X. Ding et al., Nature 615, 50 (2023)] indicates that superconductivity in nickelates is restricted to a narrow window of hydrogen concentration: 0.22 < x < 0.28 in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$H$_{x}$. This reported necessity of hydrogen suggests that it plays a crucial role for superconductivity, as it does in the vast field of hydride superconductors. Using density-functional theory and its extensions, we explore the effect of topotactic hydrogen on the electronic structure and phonon-mediated superconductivity in nickelate superconductors. Our calculations show that the electron-phonon coupling in hydrogen-intercalated nickelates is not strong enough to drive the electron pairing, and thus cannot explain the reported superconductivity., Comment: 3 figures, 1 table

The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy, but other types of behaviours are suppressed by disorder. Here, we compare the dynamics of quasiparticles under strong electric fields in aligned and random CNT networks using a combination of terahertz emission and photocurrent experiments and out-of-equilibrium numerical simulations. We find that the degree of alignment strongly influences the excited quasiparticles' dynamics, rerouting the thermalisation pathways. This is, in particular, evidenced in the high-energy, high-momentum electronic population (probed through the formation of low energy excitons via exciton impact ionization) and the transport regime evolving from diffusive to superdiffusive., Comment: 17 pages, 5 figures

Three-particle correlators are relevant for, among others, Raman, Hall and non-linear responses. They are also required for the next order of approximations extending dynamical mean-field theory diagrammatically. We present a general formalism on how to treat these three-particle correlators and susceptibilities, and calculate the local three-particle response of the Anderson impurity model numerically. We find that genuine three-particle vertex corrections are sizable. In particular, it is not sufficient to just take the bare bubble terms or corrections based on the two-particle vertex. The full three-particle vertex must be considered., Comment: 18 pages, 18 figures

We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuous-time quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implications as well as solutions. This issue does not occur when using worm sampling or in the presence of continuous baths. However certain energy spectra can be inherently close to a discrete limit, and we explain why autocorrelation times can become very large in these cases.

Despite enormous experimental and theoretical efforts, obtaining generally accepted conclusions regarding the intrinsic magnetic and electronic properties of superconducting nickelates remains exceptionally challenging. Experiments show a significant degree of uncertainty, indicating hidden factors in the synthesized films, which call for further investigations. One of those "hidden factors" is the possibility of intercalating hydrogen during the chemical reduction process from Nd(La)NiO$_3$ to Nd(La)NiO$_2$ using CaH$_2$. While hydrogen has been detected in experimental samples, not much is known about its distribution through the crystal and its influence on the electronic environment. Here, we show the tendency toward the formation of one-dimensional hydrogen chains in infinite-layers LaNiO$_2$ superconductors using density-functional theory (DFT) supplemented by dynamical mean-field theory (DMFT). The formation of such hydrogen chains induces a coexistence of different oxidation states of Ni and competing magnetic phases, and possibly explains the recently observed charge order states in nickelate superconductors. Furthermore, it contributes to the difficulty of synthesizing homogeneous nickelates and determining their ground states. The smoking gun to detect excess hydrogen in nickelates are flat phonon modes, which are infrared active and quite insensitive to the exact arrangement of the H atoms., Comment: 19 pages, 13 figures, under PRB review

This Chapter of the J\"ulich Summer School 2022 provides for a first reading on diagrammatic extensions of dynamical-mean-field theory and their application to spin fluctuations, pseudogap physics and supercondcutivtiy. The contents is as follows: 1 Introduction 2 Dynamical vertex approximation 3 Ladder dynamical vertex approximation 4 Hubbard model, cuprates and nickelates 5 Spin fluctuations 6 Pseudogap 7 Superconductivity 8 Conclusion and outlook, Comment: Chapter of Dynamical Mean-Field Theory of Correlated Electrons, Reihe: Modeling and Simulations}, Vol.~12 (Forschungszentrum J\"ulich, 2022). E. Pavarini, E. Koch, D. Vollhardt, and A. I. Lichtenstein (Eds.)

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature $T_{\rm c}$ as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high $T_{\rm c}$ to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr$_2$PdO$_3$ and $A^{\prime}_2$PdO$_2$Cl$_2$ ($A^{\prime}$=Ba$_{0.5}$La$_{0.5}$), to be virtually optimal, while others, such as NdPdO$_2$, are too weakly correlated., Comment: 8+16 pages, 5+18 figures

The vanguard of many-body theory is nowadays dealing with the full frequency dynamics of n-point Green's functions for n higher than two. Numerically, these objects easily become a memory bottleneck, even when working with discrete imaginary-time Matsubara frequencies. Here, we use the intermediate representation (IR) to compactify the two-point Green's function and three-point Fermion-Bose vertex directly on the real frequency axis, on the basis of numerical renormalization group (NRG) data. We empirically observe an upper bound of the relative error when comparing the IR reconstructed signal with the original NRG data, and demonstrate that a IR compacification is possible., Comment: 15 pages, 12 figures

We derive the exact reduced density matrix for the electrons in an analytically solvable electron-phonon model. Here, the electrons are described as a Luttinger liquid that is coupled to Einstein phonons. We further derive analytical expressions for the electron-phonon entanglement, its spectrum and mutual information at finite and zero temperature as well as for excited states. The entanglement entropy is additive in momentum for the quasi-particle excited states, but not in the electron-phonon coupled eigenmodes of the system., Comment: 9 pages, 4 figures

Superconductivity has entered the nickel age marked by enormous experimental and theoretical efforts. Notwithstanding, synthesizing nickelate superconductors remains extremely challenging, not least due to incomplete oxygen reduction and topotactic hydrogen. Here, we present density-functional theory calculations, identify a phonon mode as a possible indication for topotactic hydrogen and discuss the charge redistribution patterns around oxygen and hydrogen impurities., Comment: Paper solicited for the special issue 'New Spin on Metal-Insulator Transitions' of Crystals

We review recent studies for superconductivity using diagrammatic extensions of dynamical mean field theory. These approaches take into account simultaneously both, the local correlation effect and spatial long-range fluctuations, which are essential to describe unconventional superconductivity in a quasi-two-dimensional plane. The results reproduce and predict the experimental phase diagrams of strongly correlated system such as cuprates and nickelates. Further studies reveal that the dynamical screening effect of the pairing interaction vertex has dramatic consequences for the transition temperature and may even support exotic mechanisms like odd-frequency pairing. We also discuss the dimensionality of layered materials and how to interpret the numerical results in two dimensions., Comment: 25 pages, 8 figures

Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns. Traditionally, ranking is done by bisectioning search, which has poor cache performance on modern machines. We instead propose to use tries (prefix trees), thereby achieving a two- to ten-fold speed-up in numerical experiments with only moderate memory overhead. For the important problem of ranking permutations, the corresponding tries can be compressed. These compressed "staggered" lookups allow for a considerable speed-up while retaining the memory requirements of prior algorithms based on the combinatorial number system.

Thin films of transition metal oxides open up a gateway to nanoscale electronic devices beyond silicon characterized by novel electronic functionalities. While such films are commonly prepared in an oxygen atmosphere, they are typically considered to be ideally terminated with the stoichiometric composition. Using the prototypical correlated metal SrVO$_3$ as an example, it is demonstrated that this idealized description overlooks an essential ingredient: oxygen adsorbing at the surface apical sites. The oxygen adatoms, which persist even in an ultrahigh vacuum environment, are shown to severely affect the intrinsic electronic structure of a transition metal oxide film. Their presence leads to the formation of an electronically dead surface layer but also alters the band filling and the electron correlations in the thin films. These findings highlight that it is important to take into account surface apical oxygen or -- mutatis mutandis -- the specific oxygen configuration imposed by a capping layer to predict the behavior of ultrathin films of transition metal oxides near the single unit-cell limit.

Many metallic transition-metal oxides turn insulating when grown as films that are only a few unit-cells thick. The microscopic origins of these thickness induced metal-to-insulator transitions however remain under dispute. Here, we simulate the extreme case of a monolayer of an inconspicuous correlated metal -- the strontium vanadate SrVO$_3$ -- deposited on a SrTiO$_3$ substrate. Crucially, our system can have a termination to vacuum consisting of either a SrO or a VO$_2$ top layer. While we find that both lead to Mott insulating behavior at nominal stoichiometry, the phase diagram emerging upon doping -- chemically or through an applied gate voltage -- is qualitatively different. Indeed, our many-body calculations reveal a cornucopia of nonlocal fluctuations associated with (in)commensurate antiferromagnetic, ferromagnetic, as well as stripe and checkerboard orbital ordering instabilities. Identifying that the two geometries yield crystal-field splittings of opposite signs, we elucidate the ensuing phases through the lens of the orbital degrees of freedom. Quite generally, our work highlights that interface and surface reconstruction and the deformation or severing of coordination polyhedra in ultra-thin films drive rich properties that are radically different from the material's bulk physics., Comment: 10 pages, 8 figures

We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model we identify the one-band Hubbard model for the Ni 3$d_{x^2-y^2}$ orbital plus a pocket around the $A$-momentum. The latter however merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from {nominal} Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by experiment, indicate that the $\Gamma$ pocket, Nd 4$f$ orbitals, oxygen 2$p$ and {the} other Ni 3$d$ orbitals are not relevant in the superconducting doping regime. The physics is completely different if topotactic hydrogen is present or the oxygen reduction is incomplete. Then, a two-band physics hosted by the Ni 3$d_{x^2-y^2}$ and 3$d_{3z^2-r^2}$ orbitals emerges. Based on our minimal modeling we calculated the superconducting $T_c$ vs. Sr-doping $x$ phase diagram prior to experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as $T_c$, the agreement with experiment is astonishingly good. The prediction that $T_c$ is enhanced with pressure or compressive strain, has been confirmed experimentally as well. This supports that the one-band Hubbard model plus an electron reservoir is the appropriate minimal model., Comment: 20 pages; 9 figuress; 3 tables; to be published in Frontiers in Physics as part of a series on nickelate superconductors

We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny., Comment: 36 pages, 14 figures, resubmission to SciPost

We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show pronounced changes in the double occupation and spin energy. This analysis reveals that the loss of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections., Comment: 21 pages, 16 figures

We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice of the time steps. As a basis for step selection, asymptotically correct defect-based estimators of the local error are employed. We analyze the error of the numerical approximation in the presence of the unsmooth external potential and demonstrate the advantages of the adaptive approach.

Motivated by the recent discovery of superconductivity in the pentalayer nickelate Nd$_6$Ni$_5$O$_{12}$ [Nature Materials 10.1038], we calculate its electronic structure and superconducting critical temperature. We find that electronic correlations are essential for pushing Nd$_6$Ni$_5$O$_{12}$ into the superconducting doping range as they shift the electron pockets above the Fermi energy. As a consequence, Nd$_6$Ni$_5$O$_{12}$ can be described with a single $d_{x^2-y^2}$ orbital per Ni. Instead, for the bilayer nickelate Nd$_3$Ni$_2$O$_6$ we find correlations to drive the system into a three-orbital regime also involving the Ni $d_{xz,yz}$ states. We suggest, however, that single-orbital physics with optimal doping can be restored by substituting 60% of the trivalent Nd or La by tetravalent Zr., Comment: 16 pages totally, 4 figures in main text and 9 figures in supplementary materials

All previous cuprate superconductors display a set of common features: (i) vicinity to a Cu 3$d^{9}$ configuration; (ii) separated CuO$_2$ planes; (iii) superconductivity for doping $\delta \sim$ 0.1$-$0.3. Recently [PNAS {\bf 24}, 12156 (2019)] challenged this picture by discovering "highly overdoped" superconducting Ba$_2$CuO$_{3+y}$. Using density-functional theory + dynamical mean-field theory, we reveal a bilayer structure of Ba$_2$CuO$_{3.2}$ of alternating quasi 2D and quasi 1D character. Correlations tune an inter-layer self-doping leading to an almost half-filled, strongly nested quasi 1D $d_{b^2-c^2}$ band, which is prone to strong antiferromagnetic fluctuations, possibly at the origin of superconductivity in Ba$_2$CuO$_{3+y}$.

Excitonic effects in 1D semiconductors can be qualitatively different from those in higher dimensions. In particular, the Sommerfeld factor, the ratio of the above-band-edge excitonic continuum absorption to free electron-hole pair generation, has been shown to be less than 1 (i.e., suppressed) in 1D systems while it is larger than1 (i.e., enhanced) in 2D and 3D systems. Strong continuum suppression indeed exists in semiconducting single-wall carbon nanotubes, a prototypical 1D semiconductor. However, absorption spectra for carbon nanotubes are typically fit with a combination of Lorentzians and a polynomial background baseline with little physical meaning. Here, we performed absorption measurements in aligned single-chirality (6,5) carbon nanotube films. The obtained spectra were fit with our theoretical model obtained by solving the Boltzmann scattering equation (i.e., the quantum Fokker-Planck equation), involving fifty-nine different types of transitions among three different types of quasiparticles. Specifically, we took into account microscopic interactions between photons, phonons, and excitons, including their dispersions, which unambiguously demonstrated that the background absorption is due to phonon-assisted transitions from the semiconductor vacuum to finite-momentum continuum states of excitons. The excellent agreement we obtained between experiment and theory suggests that our numerical technique can be seamlessly extended to compute strongly out-of-equilibrium many-body dynamics and time-resolved spectra in low-dimensional materials.

The mechanism of the pseudogap observed in hole-doped cuprates remains one of the central puzzles in condensed matter physics. We analyze this phenomenon via a Feynman-diagrammatic inspection of the Hubbard model. Our approach captures the pivotal interplay between Mott localization and Fermi surface topology beyond weak-coupling spin fluctuations, which would open a spectral gap near hot spots. We show that strong coupling and particle-hole asymmetry trigger a very different mechanism: a large imaginary part of the spin-fermion vertex promotes damping of antinodal fermions and, at the same time, protects the nodal Fermi arcs (antidamping). Our analysis naturally explains puzzling features of the pseudogap observed in experiments, such as Fermi arcs being cut off at the antiferromagnetic zone boundary and the subordinate role of hot spots., Comment: 7 pages

We present the Python package ana_cont for the analytic continuation of fermionic and bosonic many-body Green's functions by means of either the Pade approximants or the maximum entropy method. The determination of hyperparameters and the implementation are described in detail. The code is publicly available on GitHub, where also documentation and learning resources are provided., Comment: 20 pages, 6 figures, open source code at https://github.com/josefkaufmann/ana_cont

Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential equations (ODE)s of Schr\"odinger type, which can be solved numerically by exponential time integrators of Magnus type. The efficiency may be enhanced by combining these with operator splittings. We will discuss several different approaches of employing exponential-based methods in conjunction with an adaptive Lanczos method for the evaluation of matrix exponentials and compare their accuracy and efficiency. For each integrator, we use defect-based local error estimators to enable adaptive time-stepping. This serves to reliably control the approximation error and reduce the computational effort

The kagome Hubbard model (KHM) is a paradigmatic example of a frustrated two-dimensional model. While its strongly correlated regime, described by a Heisenberg model, is of topical interest due to its enigmatic prospective spin-liquid ground state, the weakly and moderately correlated regimes remain largely unexplored. Motivated by the rapidly growing number of metallic kagome materials (e.g., Mn$_3$Sn, Fe$_3$Sn$_2$, FeSn, Co$_3$Sn$_2$S$_2$, Gd$_3$Ru$_4$Al$_{12}$), we study the respective regimes of the KHM by means of three complementary numerical methods: the dynamical mean-field theory (DMFT), the dynamical vertex approximation (D$\Gamma$A), and determinant quantum Monte Carlo (DQMC). In contrast to the archetypal square-lattice, we find no tendencies towards magnetic ordering, as magnetic correlations remain short-range. Nevertheless, the magnetic correlations undergo a remarkable crossover as the system approaches the metal-to-insulator transition. The Mott transition itself does however not affect the magnetic correlations. Our equal-time and dynamical structure factors can be used as a reference for inelastic neutron scattering experiments on the growing family of metallic kagome materials., Comment: 18 pages, 14 figures

Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional correlated electron systems. Here we study the arguably simplest version of these $\pi$-tons based on the semi-analytical random phase approximation (RPA) ladder in the transversal particle-hole channel. The vertex corrections to the optical conductivity are calculated directly for real frequencies. We validate that the RPA qualitatively reproduces the {\pi}-ton vertex corrections to the Drude peak in the Hubbard model. Depending on the temperature we find vertex corrections to broaden or sharpen the Drude peak., Comment: 26 pages, 25 figures; Updated to version accepted by PRB

We present and implement a self-consistent D$\Gamma$A approach for multi-orbital models and ab initio materials calculations. It is applied to the one-band Hubbard model at various interaction strengths with and without doping, to the two-band Hubbard model with two largely different bandwidths, and to SrVO$_3$. The self-energy feedback reduces critical temperatures compared to dynamical mean-field theory, even to zero temperature in two-dimensions. Compared to a one-shot, non-self-consistent calculation the non-local correlations are significantly reduced when they are strong. In case non-local correlations are weak to moderate as for SrVO$_3$, one-shot calculations are sufficient., Comment: 21 Pages, 20 Figures

Transparent conductors-nearly an oxymoron-are in pressing demand, as ultra-thin-film technologies become ubiquitous commodities. As current solutions rely on non-abundant elements, perovskites such as SrVO3 and SrNbO3 have been suggested as next generation transparent conductors. Our ab-initio calculations and analytical insights show, however, that reducing the plasma frequency below the visible spectrum by strong electronic correlations-a recently proposed strategy-unavoidably comes at a price: an enhanced scattering and thus a substantial optical absorption above the plasma edge. As a way out of this dilemma we identify several perovskite transparent conductors, relying on hole doping, somewhat larger bandwidths and separations to other bands.

The parquet formalism and Hedin's $GW\gamma$ approach are unified into a single theory of vertex corrections, corresponding to an exact reformulation of the parquet equations in terms of boson exchange. The method has no drawbacks compared to previous parquet solvers but has the significant advantage that the vertex functions decay quickly with frequencies and with respect to distances in real space. These properties coincide with the respective separation of the length and energy scales of the two-particle correlations into long/short-ranged and high/low-energetic., Comment: 14 pages, 9 figures

The two-dimensional nature of engineered transition-metal ultra-thin oxide films offers a large playground of yet to be fully understood physics. Here, we study pristine SrVO$_3$ monolayers that have recently been predicted to display a variety of magnetic and orbital orders. Above all ordering temperatures, we find that the associated non-local fluctuations lead to a momentum differentiation in the self-energy, particularly in the scattering rate. In the one-band 2D Hubbard model, momentum-selectivity on the Fermi surface ("$k=k_F$") is known to lead to pseudogap physics. Here instead, in the multi-orbital case, we evidence a differentiation between momenta on the occupied ("$kk_F$") of the Fermi surface. Our work, based on the dynamical vertex approximation, complements the understanding of spectral signatures of non-local fluctuations, calls to (re)examine other ultra-thin oxide films and interfaces with methods beyond dynamical mean-field theory, and may point to correlation-enhanced thermoelectric effects., Comment: 12 pages, 9 figures

We perform time-resolved exact diagonalization of the Hubbard model with time dependent hoppings on small clusters of up to $12$ sites. Here, the time dependence originates from a classic electromagnetic pulse, which mimics the impact of a photon. We investigate the behavior of the double occupation and spectral function after the pulse for different cluster geometries and on-site potentials. We find impact ionization in all studied geometries except for one-dimensional chains. Adding next-nearest neighbor hopping to the model leads to a significant enhancement of impact ionization, as does disorder and geometric frustration of a triangular lattice., Comment: 16 pages, 25 figures

We employ the jackknife algorithm to analyze the propagation of the statistical quantum Monte Carlo error through the Bethe--Salpeter equation. This allows us to estimate the error of dynamical mean-field theory calculations of the susceptibility and of dynamical vertex approximation calculations of the self-energy. We find that the different frequency components of the susceptibility are uncorrelated, whereas those of the self-energy are correlated. For improving the quality of the correlation matrix taking sufficiently many jackknife bins is key, while for reducing the standard error of the mean sufficiently many Monte Carlo measurements are necessary. We furthermore show that even in the case of the self-energy, the finite covariance does not have a sizable influence on the analytic continuation., Comment: 11 pages, 13figures