Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods. arXiv:1505.02290v2 [cond-mat.str-el] 15
We present an approach that combines the local density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane waves (FLAPW) method. Wannier-like functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund's coupling are calculated from a first-principle constrained RPA scheme. We apply this LDA+DMFT implementation, in conjunction with a continuous-time quantum Monte-Carlo algorithm, to the study of electronic correlations in LaFeAsO. Our findings support the physical picture of a metal with intermediate correlations. The average value of the mass renormalization of the Fe 3d bands is about 1.6, in reasonable agreement with the picture inferred from photoemission experiments. The discrepancies between different LDA+DMFT calculations (all technically correct) which have been reported in the literature are shown to have two causes: i) the specific value of the interaction parameters used in these calculations and ii) the degree of localization of the Wannier orbitals chosen to represent the Fe 3d states, to which many-body terms are applied. The latter is a fundamental issue in the application of many-body calculations, such as DMFT, in a realistic setting. We provide strong evidence that the DMFT approximation is more accurate and more straightforward to implement when well-localized orbitals are constructed from a large energy window encompassing Fe-3d, As-4p and O-2p, and point out several difficulties associated with the use of extended Wannier functions associated with the low-energy iron bands. Some of these issues have important physical consequences, regarding in particular the sensitivity to the Hund's coupling.
We investigate transport in strongly correlated metals. Within dynamical mean-field theory, we calculate the resistivity, thermopower, optical conductivity and thermodynamic properties of a hole-doped Mott insulator. Two well-separated temperature scales are identified: T(FL) below which Landau Fermi liquid behavior applies, and T(MIR) above which the resistivity exceeds the Mott-Ioffe-Regel value and bad-metal behavior is found. We show that quasiparticle excitations remain well defined above T(FL) and dominate transport throughout the intermediate regime T(FL) ~ T ~ T(MIR). The lifetime of these resilient quasiparticles is longer for electronlike excitations and this pronounced particle-hole asymmetry has important consequences for the thermopower. The crossover into the bad-metal regime corresponds to the disappearance of these excitations and has clear signatures in optical spectroscopy.
International audienceWe present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it
We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various applications within the dynamical mean-field theory (DMFT) framework. The method provides a more compact representation of the Green's functions than standard Matsubara frequencies and therefore significantly reduces the memory-storage size of these quantities. Moreover, it can be used as an efficient noise filter for various physical quantities within the continuous-time quantum Monte Carlo impurity solvers recently developed for DMFT and its extensions. In particular, we show how to use it for the computation of energies in the context of realistic DMFT calculations in combination with the local density approximation to the density functional theory (LDA+DMFT) and for the calculation of lattice susceptibilities from the local irreducible vertex function.PACS numbers: 71.27.+a, 71.10.Fd In recent years, significant progress has been made in the study of strongly-correlated fermionic quantum systems with the development of methods combining systematic analytical approximations and modern numerical algorithms. The Dynamical Mean-Field Theory (DMFT) (for a review see Ref. 1) and its various extensions. 2-6serve as successful examples for this theoretical advance. On the technical side, important progress was made in the solution of quantum impurity problems, i.e. local quantum systems coupled to a bath (self-consistently determined in the DMFT formalism). In particular, a new generation of continuous-time quantum Monte Carlo (CTQMC) impurity solvers 7-10 has emerged that provide unprecedented efficiency and accuracy (for a recent review, see Ref. 11).In practice, several important technical issues still remain. Firstly, while the original DMFT formalism is expressed in terms of single-particle quantities (Green's function and self-energy), two-particle quantities play a central role in the formulation of some DMFT extensions (e.g. dual-fermions 4,12-14 , DΓA 3 ) and in susceptibility and transport computations in DMFT itself. They typically depend on three independent times or frequencies, and spatial indices. Therefore, they are quite large objects that are hard to store, manipulate and analyze, even with modern computing capabilities. Developing more compact representations of these objects and using them to solve, e.g., the Bethe-Salpeter equations is therefore an important challenge.A natural route is to use an orthogonal polynomial representation of the imaginary-time dependence of these objects. While the application of orthogonal polynomials has had productive use in other approaches to correlated electrons, 15,16 in this paper we show how to use Legendre polynomials to represent various imaginary-time Green's functions in a more compact way and show their usefulness in some concrete calculations.A second aspect is that modern CTQMC impurity solvers still have limitations. One well-known problem is the high-fre...
Cluster dynamical mean-field calculations based on 2-, 4-, 8-and 16-site clusters are used to analyze the doping-driven metal-insulator transition in the two-dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole-doped side than on the electron-doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-Tc cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi-liquid renormalizations are larger and the electron self-energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap on some parts of the Fermi surface but gapless behavior in other parts. On the electron-doped side the partially gapped regime does not occur, and the momentum dependence of the electron self-energy is less pronounced. Implications for the high-Tc cuprates and for the use of cluster dynamical mean-field methods in wider classes of problems are discussed.
The Luttinger-Ward functional Φ [G], which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function G, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy Σ[G] ∝ δΦ[G]/δG is not a single-valued functional of G: in addition to the physical solution for Σ [G], there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for Σ in terms of G is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green's function G0 converges to the correct physical branch of Σ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series.
We present an approach to the normal state of cuprate superconductors which is based on a minimal cluster extension of dynamical mean-field theory. Our approach is based on an effective two-impurity model embedded in a self-consistent bath. The two degrees of freedom of this effective model can be associated to the nodal and antinodal regions of momentum space. We find a metal-insulator transition which is selective in momentum space: At low doping quasiparticles are destroyed in the antinodal region, while they remain protected in the nodal region, leading to the formation of apparent Fermi arcs. We compare our results to tunneling and angular-resolved photoemission experiments on cuprates. At very low energy, a simple description of this transition can be given using rotationally invariant slave bosons.
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