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We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping [D. Rybicki et al., Nat. Commun. 7, 1–6 (2016)]. They have also shown that a large charge-transfer gap [W. Ruan et al., Sci. Bull. (Beijing) 61, 1826–1832 (2016)], a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role among doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen. Experiments [L. Wang et al., arXiv [Preprint] (2020). https://arxiv.org/abs/2011.05029 (Accessed 10 November 2020)] also suggest that superexchange is at the origin of superconductivity in cuprates. Our results reveal the consistency of these experiments with the above two experimental findings. Indeed, we show that covalency and a charge-transfer gap lead to an effective short-range superexchange interaction between copper spins that ultimately explains pairing and superconductivity in the three-band Hubbard model of cuprates.

The similarity in mechanical properties of dense active matter and sheared amorphous solids has been noted in recent years without a rigorous examination of the underlying mechanism. We develop a mean-field model that predicts that their critical behavior—as measured by their avalanche statistics—should be equivalent in infinite dimensions up to a rescaling factor that depends on the correlation length of the applied field. We test these predictions in two dimensions using a numerical protocol, termed “athermal quasistatic random displacement,” and find that these mean-field predictions are surprisingly accurate in low dimensions. We identify a general class of perturbations that smoothly interpolates between the uncorrelated localized forces that occur in the high-persistence limit of dense active matter and system-spanning correlated displacements that occur under applied shear. These results suggest a universal framework for predicting flow, deformation, and failure in active and sheared disordered materials.

Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of nonlinear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green's function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green's function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.

How is the irreversibility of a high-dimensional chaotic system related to its dynamical behavior? In this paper, we address this question by developing a stochastic-thermodynamics treatment of complex networks that exhibit chaos. Specifically, we establish an exact relation between the averaged entropy production rate—a measure of irreversibility—and the autocorrelation function for an infinite system of neurons coupled via random non-reciprocal interactions. We show how, under given noise strength, the entropy production rate can signal the onset of a transition occurring as the coupling heterogeneity increases beyond a critical value via a change in its functional form upon crossing this point. Furthermore, this transition happens at a fixed, noise-independent entropy production rate, elucidating how robust energetic cost is possibly responsible for optimal information processing at criticality.

Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as \\({{U}_{pd}}\\) between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d–p orbital splitting has to be adjusted ‘ad hoc’ on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory to the prototypical case of the three-band Emery dp model for the cuprates, we demonstrate that, without any ‘ad hoc’ adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction \\({{U}_{pd}}\\). Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.

Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d-p orbital splitting has to be adjusted 'ad hoc' on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory to the prototypical case of the three-band Emery dp model for the cuprates, we demonstrate that, without any 'ad hoc' adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction . Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.

The evolution between Fermi-liquid and non-Fermi-liquid states in correlated electron systems has been a central subject in condensed matter physics because of the coupled intriguing magnetic and electronic states. An effective pathway to explore the nature of non-Fermi-liquid behavior is to approach its phase boundary. Here we report a crossover from non-Fermi-liquid to Fermi-liquid state in metallicCaRuO3through ionic liquid gating induced protonation with electric field. This electronic transition subsequently triggers a reversible magnetic transition with the emergence of an exotic ferromagnetic state from this paramagnetic compound. Our theoretical analysis reveals that hydrogen incorporation plays a critical role in both the electronic and magnetic phase transitions via structural distortion and electron doping. These observations not only help understand the correlated magnetic and electronic transitions in perovskite ruthenate systems, but also provide novel pathways to design electronic phases in correlated materials.

Based on first-principles resistivity calculations, it was recently concluded that the thermal conductivity of iron in Earth’s core was too high to sustain thermal convection, thus invalidating such geodynamo models; new calculations including electron correlations find that electron–electron scattering is comparable to the electron–phonon scattering at high temperatures in iron, doubling the expected resistivity, and reviving conventional geodynamo models. Conductivity of the core Numerical calculations based on density functional theory and electron–phonon scattering have recently been used to predict that the conductivity of iron at the pressure and temperature conditions of the Earth's core is substantially higher than previously thought, to the point that it would be difficult to sustain the geodynamo with thermal convection. But now Peng Zhang et al . have combined a self-consistent density functional theory with dynamical mean-field theory, and find that electron–electron scattering is comparable to electron–phonon scattering at such high temperatures. They predict a lower conductivity for iron at core conditions compared to the earlier calculations, which is once again consistent with thermal convection driving the geodynamo. Earth’s magnetic field has been thought to arise from thermal convection of molten iron alloy in the outer core, but recent density functional theory calculations have suggested that the conductivity of iron is too high to support thermal convection 1 , 2 , 3 , 4 , resulting in the investigation of chemically driven convection 5 , 6 . These calculations for resistivity were based on electron–phonon scattering. Here we apply self-consistent density functional theory plus dynamical mean-field theory (DFT + DMFT) 7 to iron and find that at high temperatures electron–electron scattering is comparable to the electron–phonon scattering, bringing theory into agreement with experiments and solving the transport problem in Earth’s core. The conventional thermal dynamo picture is safe. We find that electron–electron scattering of d electrons is important at high temperatures in transition metals, in contrast to textbook analyses since Mott 8 , 9 , and that 4 s electron contributions to transport are negligible, in contrast to numerous models used for over fifty years. The DFT+DMFT method should be applicable to other high-temperature systems where electron correlations are important.

It has been widely recognized that, based on standard density functional theory calculations of the electron-phonon coupling, the superconducting transition temperature ( T c ) in bulk FeSe is exceptionally low (almost 0 K) within the Bardeen-Cooper-Schrieffer formalism. Yet the experimentally observed T c is much higher (∼10 K), and the underlying physical origin remains to be fully explored, especially at the quantitative level. Here we present the first accurate determination of T c in FeSe where the correlation-enhanced electron-phonon coupling is treated within first-principles dynamical mean-field theory. Our studies treat both the multiple electronic bands across the Fermi level and phononic bands, and reveal that all the optical phonon modes are effectively coupled with the conduction electrons, including the important contributions of a single breathing mode as established by previous experiments. Accordingly, each of those phonon modes contributes pronouncedly to the electron pairing, and the resultant T c is drastically enhanced to the experimentally observed range. The approach developed here should be broadly applicable to other superconducting systems where correlation-enhanced electron-phonon coupling plays an important role.