Solving the Multi-site and Multi-orbital Dynamical Mean Field Theory Using Density Matrix Renormalization (original) (raw)
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Dynamical Mean Field Theory with the Density Matrix Renormalization Group
Physical Review Letters, 2004
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Great theoretical progress in our understanding of the physics of strongly correlated electron systems has been possible since the introduction of the Dynamical Mean Field Theory (DMFT) just over ten years now . This approach is based on the natural extension of the familiar classical mean-field theory of statistical mechanics to the treatment of models of strongly interacting electrons on a lattice. The DMFT solution of the model is exact in the limit of large lattice dimensionality or large connectivity [2, 3]. Since its introduction, DMFT has been widely adopted and was used for the investigation of a large variety of model Hamiltonians relevant for problems as diverse as colossal magneto-resistance, heavy fermions, metal-insulator transitions, etc. . A great deal of interest is currently centered around the ongoing efforts to incorporate DMFT as the local correlation physics "engine" for first-principle calculations of realistic compounds . At the heart of the DMFT method is the solution of an associated quantum impurity model where the environment of the impurity has to be determined self-consistently. Therefore the ability to obtain reliable DMFT solutions of lattice model Hamiltonians relies directly on the ability to solve quantum impurity models. Since solutions of general impurity models are usually not analytically tractable, one has to resort to numerical algorithms or approximate methods. Among the a priori exact numerical algorithms available we count the Hirsch-Fye Quantum Monte Carlo [6] method and Wilson's Numerical Renormalization Group (NRG) . The former is a finite-temperature method that is formulated in imaginary time and has been applied to a large variety of impurity models including the multi-orbital case that corresponds to correlated multi-band lattice Hamiltoni- * Present address: DFMC, Unicamp, Campinas, São Paulo, Brasil.
Chinese Physics B, 2010
An impurity solver for the dynamical mean field (DMFT) study of the Mott insulators is proposed, which is based on the second order perturbation of the hybridization function. After carefully benchmarking it with Quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, we conclude that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA+DMFT studies of the Mott insulators with long range order.
Validity of the local self-energy approximation: application to coupled quantum impurities
We examine the quality of the local self-energy approximation, applied here to models of multiple quantum impurities coupled to an electronic bath. The local self-energy is obtained by solving a single-impurity Anderson model in an effective medium that is determined self-consistently, similar to the dynamical mean-field theory (DMFT) for correlated lattice systems. By comparing to exact results obtained using the numerical renormalization group, we determine situations where "impurity-DMFT" is able to capture the physics of highly inhomogeneous systems, and those cases where it fails. For two magnetic impurities separated in real-space, the onset of the dilute limit is captured, but RKKY-dominated inter-impurity singlet formation cannot be described. For parallel quantum dot devices, impurity-DMFT succeeds in capturing underscreened Kondo physics by self-consistent generation of a critical pseudogapped effective medium. However, the quantum phase transition between high- and low-spin states on tuning interdot coupling cannot be described.
Efficient real-frequency solver for dynamical mean-field theory
Physical Review B
We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks with an approximate spacing proportional to the band width divided by the number of bath sites. The self-consistency cycle is performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on ligand field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling, and low-symmetry crystal fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.
Fast multi-orbital equation of motion impurity solver for dynamical mean field theory
Journal of Physics: Condensed Matter, 2011
We propose a fast multi-orbital impurity solver for the dynamical mean field theory (DMFT). Our DMFT solver is based on the equations of motion (EOM) for local Green's functions and constructed by generalizing from the single-orbital case to the multi-orbital case with inclusion of the inter-orbital hybridizations and applying a mean field approximation to the inter-orbital Coulomb interactions. The two-orbital Hubbard model is studied using this impurity solver within a large range of parameters. The Mott metal-insulator transition and the quasiparticle peak are well described. A comparison of the EOM method with the QMC method is made for the two-orbital Hubbard model and a good agreement is obtained. The developed method hence holds promise as a fast DMFT impurity solver in studies of strongly correlated systems.
Physical Review Letters
We show that the numerical renormalization group (NRG) is a viable multi-band impurity solver for Dynamical Mean Field Theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund's metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transfered from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
Spectral Density Functional Approach to Electronic Correlations and Magnetism in Crystals
Electron Correlations and Materials Properties 2, 2002
A novel approach to electronic correlations and magnetism of crystals based on realistic electronic structure calculations is reviewed. In its simplest form it is a combination of the "local density approximation" (LDA) and the dynamical mean field theory (DMFT) approaches. Using numerically exact QMC solution to the effective DMFT multi-orbital quantum-impurity problem, a successful description of electronic structure and finite temperature magnetism of transition metals has been achieved. We discuss a simplified perturbation LDA+DMFT scheme which combines the T-matrix and fluctuation-exchange approximation (TM-FLEX). We end with a discussion of cluster generalization of the non-local DMFT scheme and its applications to the magnetism and superconductivity of high-Tc superconductors.
Numerical renormalization group method for quantum impurity systems
In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group ͑NRG͒ method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory. 441 B. Periodic Anderson and Kondo lattice models 442 C. Lattice models with phonons 444 VI. Summary 445 Acknowledgments 446 References 446