Fast multi-orbital equation of motion impurity solver for dynamical mean field theory

Feng, Qingguo; Oppeneer, Peter M.

doi:10.1088/0953-8984/23/42/425601

Cited by 4 publications

(13 citation statements)

References 36 publications

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“…At lower temperatures, both NCA and OCA show spurious non-Fermi liquid behavior, leading to artifacts in the spectra. 13,14 Many other approximate schemes for solving the AIM exist, [15][16][17][18][19] though all are burdened with some kind of limitation.…”

Section: Introductionmentioning

confidence: 99%

Kondo physics of the Anderson impurity model by distributional exact diagonalization

2016

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The Distributional Exact Diagonalization (DED) scheme is applied to the description of Kondo physics in the Anderson impurity model. DED maps Anderson's problem of an interacting impurity level coupled to an infinite bath onto an ensemble of finite Anderson models, each of which can be solved by exact diagonalization. An approximation to the self-energy of the original infinite model is then obtained from the ensemble averaged self-energy. Using Friedel's sum rule, we show that the particle number constraint, a central ingredient of the DED scheme, ultimately imposes Fermi liquid behavior on the ensemble averaged self-energy, and thus is essential for the description of Kondo physics within DED. Using the Numerical Renormalization Group (NRG) method as a benchmark, we show that DED yields excellent spectra, both inside and outside the Kondo regime for a moderate number of bath sites. Only for very strong correlations (U/Γ 10) does the number of bath sites needed to achieve good quantitative agreement become too large to be computationally feasible.

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Section: Introductionmentioning

confidence: 99%

Kondo physics of the Anderson impurity model by distributional exact diagonalization

2016

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“…In the DMFT, the main tasks are solving the so-called impurity problem and deriving the DMFT self-consistency conditions for a specified lattice of a real material. For the former task, several numerical techniques have been developed for constructing the impurity solver, e.g., the quantum Monte Carlo (QMC) method [5], the exact diagonalization (ED) method [6,7], the numerical renormalization group (NRG) method [8,9], the density matrix renormalization group (DMRG) method [10], the continuous time quantum Monte Carlo (CTQMC) method [11,12], and the equation of motion (EOM) method [13][14][15]. The EOM method, which is the focus of the present article, works directly on the real frequency axis and for any temperature.…”

Section: Introductionmentioning

confidence: 99%

“…A finite-U single-orbital impurity solver with spin-orbital degeneracy N has been developed in [14]. Recently, a multi-orbital equation of motion (MO-EOM) impurity solver has been developed by us in [15], which correctly captures the physics of some many-body systems. However, in [15] we have used the mean field approximation for the on-site inter-orbital Coulomb interactions and have neglected the inter-orbital fluctuations.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a multi-orbital equation of motion (MO-EOM) impurity solver has been developed by us in [15], which correctly captures the physics of some many-body systems. However, in [15] we have used the mean field approximation for the on-site inter-orbital Coulomb interactions and have neglected the inter-orbital fluctuations. This is approximately valid only for those systems where the inter-orbital effects are weak or there exists strong screening.…”

Section: Introductionmentioning

confidence: 99%

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An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach

Feng

Oppeneer²

2012

J. Phys.: Condens. Matter

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We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory (DMFT) based on equations of motion (EOM) of Green's functions and decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, involving the interorbital fluctuations. As an example of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison substantiates a good agreement, but also reveals a dissimilar behavior in the densities of states (DOS) which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the value of the EOM method for the study of multi-orbital strongly correlated systems.

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“…Recently we have numerically studied 10,11 the first three terms in Eq. (1) within the dynamical mean field theory (DMFT).…”

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Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

Feng¹,

Oppeneer²

2012

Phys. Rev. B

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A general multi-orbital Hubbard model, which includes on-site inter-orbital electron hoppings, is introduced and studied. It is shown that the on-site inter-orbital single electron hopping is one of the most basic interactions. Two electron spin-flip and pair-hoppings are shown to be correlation effects of higher order than the on-site inter-orbital single hopping. It is shown how the double and higher hopping interactions can be well-defined for arbitrary systems. The two-orbital Hubbard model is studied numerically to demonstrate the influence of the single electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site inter-orbital hopping suppresses the so-called orbital-selective Mott transition.PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h Strongly correlated electron systems have drawn great interest, as they exhibit many exotic phenomena, such as metal-insulator transitions, unusual forms of magnetism, superconductivity, and heavy-fermion behavior.1,2 These systems are therefore investigated theoretically in both model and ab initio calculations. One of the most essential tasks is to model the system appropriately, i.e., such that a realistic physical picture can be attained. In condensed matter theory the Hubbard model, which was originally proposed in the early sixties, 3-5 is one of the simplest, yet also the most important and most frequently studied lattice model to investigate strongly correlated electron systems. It sets up a competition between an inter-site quantum mechanical hopping term and an on-site Coulomb interaction term. As a consequence the model can describe various non-trivial phenomena. Due to its simplicity and because the model has captured the essence of strongly correlated electron systems, the Hubbard model has been widely used. 6-9In a realistic situation an atom in a correlated system will usually have several partial filled orbitals and should therefore be described with a multi-orbital (MO) Hubbard model. With the inclusion of orbital degrees of freedom, inter-orbital interactions have to be included for such a system. The inter-site hoppings should now be a sum of the inter-site intra-orbital hoppings and the inter-site inter-orbital hoppings, where the two kinds of hopping are defined according to the orbital indices of the start and the end orbitals for hopping electron are identical or not, respectively. Moreover, besides the remain competition of the inter-site hopping and on-site Coulomb interactions, one new kind of on-site interactions will join into this competition, i.e., the on-site inter-orbital hoppings. Acting as the inter-site hoppings, the on-site inter-orbital hoppings are also associated to the kinetic energy of electrons. All the inter-site hoppings, on-site inter-orbital hoppings and on-site Coulomb interactions (which also divides as on-site intra-orbital Coulomb interactions and on-site inter-orbital Coulomb interactions) constitute a competition for various inter...

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Fast multi-orbital equation of motion impurity solver for dynamical mean field theory

Cited by 4 publications

References 36 publications

Kondo physics of the Anderson impurity model by distributional exact diagonalization

Kondo physics of the Anderson impurity model by distributional exact diagonalization

An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach

Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

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