Validity of the local approximation in iron pnictides and chalcogenides

Abstract

We introduce a cluster DMFT (Dynamical Mean Field Theory) approach to study the normal state of the iron pnictides and chalcogenides. In the regime of moderate mass renormalizations, the self-energy is very local, justifying the success of single site DMFT for these materials and for other Hunds metals. We solve the corresponding impurity model with CTQMC (Continuous Time Quantum Monte-Carlo) and find that the minus sign problem is not severe in regimes of moderate mass renormalization.The unexpected discovery of superconductivity in the iron pnictide based materials has opened a new era of research in the field of condensed matter physics.[1] Multiple approaches, starting from weak coupling such as the random phase approximation (RPA) and strong coupling approaches using lessons learned from the t-J model, have been proposed, but there is not yet consensus in the community of what constitutes the proper theoretical framework for describing these systems.[2] It has been proposed that iron pnictides and chalcogenides are important not only because of their high temperature superconductivity, but because their normal state properties represent a new class of strongly correlated systems, the Hunds metals. They are distinct from doped Mott Hubbard systems, in that correlations effects in their physical properties derive from the Hunds rule coupling J, rather than the Hubbard U. [3,4] Many other interesting Hunds metals have been recognized, as for example Ruthenates [5] and numerous 3d and 4d compounds [6].Dynamical Mean Field Theory [7](DMFT) and its cluster extensions [8,9] have provided a good starting point for the description of Mott Hubbard physics. It is now established that it describes many puzzling properties of three dimensional materials such as Vanadium oxides near their finite temperature Mott transition. [10] In materials such as cuprates, as the temperature is lowered, the description in terms of single site DMFT gradually breaks down. New phenomena such as momentum space differentiation and the opening of a pseudogap takes place, and cluster DFMT is essential. How different cluster sizes and methods captures these effects has been explored intensively. [14,29,[36][37][38][39][40][41] The iron pnictides and chalcogenides have been extensively studied using LDA+DMFT by several groups. [3,4,[42][43][44] It has been argued using the GW method, that the frequency dependence of low order diagrams in perturbation theory in these materials is very local.[45] However, because of the difficulties posed by the multiorbital nature of these compounds, the accuracy of the local approximation beyond the GW level has not been examined and is the main goal of this paper.Building on the work of Ref. 46, we introduce a cluster extension for the treatment of iron pinctides, which is numerically tractable using CTQMC. By comparing single site and cluster DMFT, we establish that in a broad range of parameters where the mass renormalizations are of the order of 2 to 3, which corresponds to the experimental situation in...

Nonlocal correlations in the orbital selective Mott phase of a one-dimensional multiorbital Hubbard model

“…58 It is expected that the local approximation will perform better in higher dimensions, since DMFT becomes exact in the limit of infinite dimensions; however, it is unclear how well the method will capture similar non-local correlations in two dimensions relevant for the Fe-based superconductors. A recent study 16 has argued that the local approximation is quite accurate for parameters relevant to the iron-based superconductors, however, it remains to be seen if this will remain true for all parameter regimes or when longer range fluctuations are included. Our results further highlight the need for the continued development of numerical methods capable of handling the strong Hubbard and Hund's interactions in intermediate dimensions and on extended clusters.…”

“…[1][2][3][4] On a theoretical front, this is a challenging problem due to a lack of non-perturbative methods for treating multiorbital Hubbard models at intermediate or strong couplings and on extended systems. Nevertheless, considerable progress has been made using mean-field-based approaches, [4][5][6][7][8][9][10][11][12][13][14][15][16] resulting in new concepts such as that of a Hund's metal 7,10,17,18 and the orbital-selective Mott phase (OSMP). 10,19 These concepts are central to our understanding the paradoxical appearance of both localized and itinerant characteristics in many multi-orbital systems 20,21 and bad metallic behavior in the presence of sizable electronic correlations.…”

“…To date, most non-perturbative studies have used cluster DMFT or the dynamical cluster approximation (DCA); 16,[31][32][33][34][35] however, these techniques are typically limited to a handful of sites when multiple orbitals are included in the basis. This is due to technical issues related to each choice in impurity solver, such as the Fermion sign problem in the case of quantum Monte Carlo or the exponential growth of the Hilbert space in the case of exact diagonalization.…”

Effect of Nonlocal Correlations on the Electronic Structure of LiFeAs

“…Consideration of momentum dependence in the selfenergy in real materials' calculations are scarce but promising, [32][33][34][35][36][37][38] showing, for instance, effects of bandwidth widening and momentum-dependent bandshifts in the systems studied 33,35,37 . Here we explore this dependence by considering an approach where spin fluctuations play the dominant role and it allows both, a description * zantout@itp.uni-frankfurt.de of local and non-local correlations on an equal footing.…”

TRILEX and GW +EDMFT approach to d -wave superconductivity in the Hubbard model

“…Finally, let us emphasize that the question of superconductivity in multi-orbital systems like iron-based superconductors is another natural application of the TRILEX method, in particular in view of the strong AF fluctuations in these compounds. In this multi-orbital case, being able to describe the SC phase without having to solve clusters (which are numerically very expensive within multi-orbital cluster DMFT 90,91 ) could prove to be very tion, Eq. 6:…”