Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling.

Abstract: We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.

Deep Learning the Functional Renormalization Group.

We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional t-t^{'} Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a neural ordinary differential equation solver in a low-dimensional latent space efficiently learns the FRG dynamics that delineates the various magnetic and d-wave superconducting regimes of the Hubbard model. We further present a dynamic mode decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the FRG dynamics. Our Letter demonstrates the possibility of using artificial intelligence to extract compact representations of the four-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength.

We study the fluctuations responsible for pairing in the d-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d-wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

Resistivity Exponents in 3D Dirac Semimetals From Electron-Electron Interaction.

We study the resistivity of three-dimensional semimetals with linear dispersion in the presence of on-site electron-electron interaction. The well-known quadratic temperature dependence of the resistivity of conventional metals is turned into an unusual T^{6} behavior. An analogous change affects the thermal transport, preserving the linearity in T of the ratio between thermal and electrical conductivities. These results hold from weak coupling up to the nonperturbative region of the Mott transition. Our findings yield a natural explanation for the hitherto not understood large exponents characterizing the temperature dependence of transport experiments on various topological semimetals.

How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems.

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

Osmates on the Verge of a Hund's-Mott Transition: The Different Fates of NaOsO_{3} and LiOsO_{3}.

We clarify the origin of the strikingly different spectroscopic properties of the chemically similar compounds NaOsO_{3} and LiOsO_{3}. Our first-principle, many-body analysis demonstrates that the highly sensitive physics of these two materials is controlled by their proximity to an adjacent Hund's-Mott insulating phase. Although 5d oxides are mildly correlated, we show that the cooperative action of intraorbital repulsion and Hund's exchange becomes the dominant physical mechanism in these materials if their t_{2g} shell is half filled. Small material specific details hence result in an extremely sharp change of the electronic mobility, explaining the surprisingly different properties of the paramagnetic high-temperature phases of the two compounds.

Doping-induced insulator-metal transition in the Lifshitz magnetic insulator NaOsO3.

By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO3. Electron doping is treated within a supercell approach by replacing sodium with magnesium at different concentrations ([Formula: see text], [Formula: see text]). Undoped NaOsO3 is subjected to a temperature-driven Lifshitz transition involving a continuous closing of the gap due to longitudinal and rotational spin fluctuations (Kim et al 2016 Phys. Rev. B 94 241113). Here we find that Mg doping suppresses the insulating state, gradually drives the system to a metallic state (via an intermediate bad metal phase) and the transition is accompanied by a progressive lowering of the Os magnetic moment. We inspected the role of longitudinal spin fluctuations by constraining the amplitude of the local Os moments and found that a robust metal state can be achieved below a critical moment. In analogy with the undoped case we conjecture that the decrease of the local moment can be controlled by temperature effects, in accordance with the theory of itinerant electron magnetism.

Electronics with Correlated Oxides: SrVO(3)/SrTiO(3) as a Mott Transistor.

We employ density functional theory plus dynamical mean field theory and identify the physical origin of why two layers of SrVO(3) on a SrTiO(3) substrate are insulating: the thin film geometry lifts the orbital degeneracy, which in turn triggers a first-order Mott-Hubbard transition. Two layers of SrVO(3) are just at the verge of a Mott-Hubbard transition and hence ideally suited for technological applications of the Mott-Hubbard transition: the heterostructure is highly sensitive to strain, electric field, and temperature. A gate voltage can also switch between metal (ON) and insulator (OFF), so that a transistor with ideal ON-OFF switching properties is realized.