We investigate the role of non-local correlations in LiFeAs by exploring an ab-initio-derived multiorbital Hubbard model for LiFeAs via the Two-Particle Self-Consistent (TPSC) approach. The multi-orbital formulation of TPSC approximates the irreducible interaction vertex to be an orbitaldependent constant, which is self-consistently determined from local spin and charge sum rules. Within this approach, we disentangle the contribution of local and non-local correlations in LiFeAs and show that in the local approximation one recovers the dynamical-mean field theory (DMFT) result. The comparison of our theoretical results to most recent angular-resolved photoemission spectroscopy (ARPES) and de-Haas van Alphen (dHvA) data shows that non-local correlations in LiFeAs are decisive to describe the measured spectral function A( k, ω), Fermi surface and scattering rates. These findings underline the importance of non-local correlations and benchmark different theoretical approaches for iron-based superconductors. arXiv:1906.11853v1 [cond-mat.str-el]

Starting from an ab initio-derived two-site dimer Hubbard hamiltonian on a triangular lattice, we calculate the superconducting gap functions and critical temperatures for representative κ-(BEDT-TTF)2X superconductors by solving the linearized Eliashberg equation using the Two-Particle Self-Consistent approach (TPSC) extended to multi-site problems. Such an extension allows for the inclusion of molecule degrees of freedom in the description of these systems. We present both, benchmarking results for the half-filled dimer model as well as detailed investigations for the 3/4filled molecule model. Remarkably, we find in the latter model that the phase boundary between the two most competing gap symmetries discussed in the context of these materials -dxy and the recently proposed eight-node s+d x 2 −y 2 gap symmetry -is located within the regime of realistic model parameters and is especially sensitive to the degree of in-plane anisotropy in the materials as well as to the value of the on-site Hubbard repulsion. We show that these results provide a more complete and accurate description of the superconducting properties of κ-(BEDT-TTF)2X than previous Random Phase Approximation (RPA) calculations and, in particular, we discuss predicted critical temperatures in comparison to experiments. Finally, our findings suggest that it may be even easier to experimentally switch between the two pairing symmetries as previously anticipated by invoking pressure, chemical doping or disorder effects.

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One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many‐body methods are required for its solution. In this review, an overview on the non‐perturbative two‐particle self‐consistent method (TPSC), which was originally introduced to describe the electronic properties of the single‐band Hubbard model, is presented. A detailed derivation of the multi‐orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean‐field theory results are discussed.

In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the importance of non-local (momentum dependent) vs. local contributions to the self-energy and show that the local self-energy provides a qualitative description of the topological phase diagrams of many-body interacting systems, whereas the explicit momentumdependence constitutes a correction to the exact location of the phase transition. For the latter, we propose a statistical analysis, on the basis of which we develop a stochastic upper bound for the uncertainty of the Chern number as a function of the amount of momentum-dependence of the self-energy. We apply this analysis to the Haldane-Hubbard model and discuss the implications of our results for a general class of many-body interacting systems.