Density-matrix functional theory of strongly correlated fermions on lattice models and minimal-basis Hamiltonians

Töws, W.; Saubanère, Matthieu; Pastor, G.

doi:10.1007/s00214-013-1422-0

Cited by 9 publications

(3 citation statements)

References 82 publications

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“…Time-dependent [49][50][51] and temperature-dependent extensions [52,53] have been investigated over the years. Other reduced quantities can also be used, as first discussed by Schönhammer et al [34], such as the 1-body reduced density matrix [54][55][56][57][58][59][60][61], or the steady current in connection with steady-state transport [62,63].…”

Section: Introductionmentioning

confidence: 99%

Site-occupation embedding theory using Bethe ansatz local density approximations

et al. 2018

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Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key densityfunctional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wavefunction has been performed with the density matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials. * Corresponding author; senjean@unistra.fr for which DMFT is not sufficiently accurate, especially in the case when non local electron correlation becomes important. In order to further improve on its performance, combined DMFT+DFT [13] or DMFT+GW [14-19] schemes have been proposed to recover such effects. In another promising approach, the so-called selfenergy embedding theory [20][21][22], strong correlation is not considered as strictly local, which can be appreciable for real compounds. Its applicability to both model and ab-initio Hamiltonians is also appealing. All these embedding techniques are formulated in terms of the (frequency-dependent) one-particle Green function. On the other hand, in the density-matrix embedding theory (DMET) [23][24][25][26][27][28][29], the embedded fragment (impurity) is described with a high-level wavefunction-based method while the rest of the system is usually treated at the mean-field level. Extensions have been proposed in order to include correlation in the bath [30] or for improving the description of the boundary between the fragment and the bath [31].Turning to DFT, its extension to model Hamiltonians is usually referred to as site-occupation functional theory (SOFT) [32][33][34][35]. In conventional Kohn-Sham (KS) SOFT, the physical fully-interacting many-body problem is mapped onto a noninteracting one by means of a Hartree-exchange-correlation (Hxc) functional of the density (i.e., the sites occupation in this context). The SOFT has been shown to give very accurate density and energy profiles with the Bethe ansatz local density approximation (BALDA) [36][37][38], the spin-dependent BALDA [39], and its fully numerical formulation [40,41]. The methods have been applied to both repulsive [42,43] and attractive [44,45] Hubbard models. arXiv:1710....

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Section: Introductionmentioning

confidence: 99%

Site-occupation embedding theory using Bethe ansatz local density approximations

et al. 2018

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“…A general discussion of the density-functional theory of lattice models and minimal basis Hamiltonians may be found in Ref. [53].…”

Section: Density-matrix Functional Theory On a Latticementioning

confidence: 99%

Interaction-energy functional of the Hubbard model: Local formulation and application to low-dimensional lattices

2016

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The interaction energy W [γ ] of the Hubbard model is regarded as a functional of the single-particle density matrix γ in the framework of lattice density-functional theory. The local character of the Hubbard interaction is exploited to express W as a sum of local contributions ω i [γ ], for which a simple semilocal scaling approximation is proposed. The method is applied to the ionic Hubbard model on one-and two-dimensional lattices with homogeneous and inhomogeneous Coulomb repulsions. Results are given for the kinetic and Coulomb energies, interatomic charge transfers, local magnetic moments, and charge gaps. Goals and limitations of the functional are discussed by comparison with exact results.

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“…An extension of BALDA to higher dimensions has been recently proposed [46]. Note also that the use of other (frequency-independent) reduced quantities, such as the one-body density matrix, has been considered in the so-called lattice DFT [47][48][49][50][51][52][53]. In recent years, an in-principle-exact alternative formulation of SOFT, referred to as site-occupation embedding theory (SOET) [54][55][56][57], has been explored.…”

Section: Introductionmentioning

confidence: 99%

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

2019

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A reformulation of site-occupation embedding theory (SOET) in terms of Green's functions is presented. Referred to as site-occupation-Green's function embedding theory (SOGET), this novel extension of density-functional theory for model Hamiltonians shares many features with dynamical mean-field theory (DMFT) but is formally exact (in any dimension). In SOGET, the impurity-interacting correlation potential becomes a density-functional self-energy which is frequency-dependent and in principle non-local. A simple local density-functional approximation (LDA) combining the Bethe Ansatz (BA) LDA with the self-energy of the two-level Anderson model is constructed and successfully applied to the one-dimensional Hubbard model. Unlike in previous implementations of SOET, no many-body wavefunction is needed, thus reducing drastically the computational cost of the method.

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Density-matrix functional theory of strongly correlated fermions on lattice models and minimal-basis Hamiltonians

Cited by 9 publications

References 82 publications

Site-occupation embedding theory using Bethe ansatz local density approximations

Site-occupation embedding theory using Bethe ansatz local density approximations

Interaction-energy functional of the Hubbard model: Local formulation and application to low-dimensional lattices

Site-occupation Green's function embedding theory: A density functional approach to dynamical impurity solvers

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