Density-Functional Theory for the Hubbard Model: Numerical Results for the Luttinger Liquid and the Mott Insulator

Capelle, K.; Lima, N. A.; Silva, M. F.; Oliveira, L. N.

doi:10.1007/978-94-017-0409-0_12

Cited by 13 publications

(16 citation statements)

References 58 publications

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“…The performance of SOET and P-SOET relies on the accuracy of the per-site correlation functional e c (n) and the impurity correlation functional E imp c,M (n), as well as their derivatives with respect to U , t and n i 49 . The LDA based on Bethe Ansatz (BA) (so-called BALDA) is used for e c (n) [56][57][58] , and is exact in the thermodynamic limit for U = 0, U → +∞ and n = 1 for any U . For Figure 1.…”

Section: Approximate Functionalsmentioning

confidence: 99%

Projected site-occupation embedding theory

Senjean

2019

Phys. Rev. B

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Site-occupation embedding theory (SOET) [B. Senjean et al., Phys. Rev. B 97, 235105 (2018)] is an in-principle exact embedding method combining wavefunction theory and density functional theory that gave promising results when applied to the one-dimensional Hubbard model. Despite its overall good performance, SOET faces a computational cost problem as its auxiliary impurityinteracting system remains the size of the full system (which is problematic as the computational cost increases exponentially with system size). In this work, this issue is circumvented by employing the Schmidt decomposition, thus leading to a drastic reduction of the computational cost while retaining the same accuracy. We show that this projected version of SOET (P-SOET) is competitive with other embedding techniques such as density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)]. In contrast to the latter, density functional contributions come naturally into play in P-SOET's framework without any additional computational cost or double counting effect. As an important result, the density-driven Mott-Hubbard transition in one dimension (which is displayed by multiple impurity sites in DMET or in dynamical mean-field theory) is well described, for the first time, with a single impurity site. arXiv:1902.05747v3 [cond-mat.str-el]

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Section: Approximate Functionalsmentioning

confidence: 99%

Projected site-occupation embedding theory

Senjean

2019

Phys. Rev. B

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“…The full curve was obtained using the densitymatrix renormalization group ͑DMRG͒, 19,20 while the dotted curve was obtained from density-functional theory ͑DFT͒ within the Bethe-Ansatz local-density approximation ͑BA-LDA͒. [21][22][23] In view of the complexity of the problem and the surprising nature of some of our conclusions, we found it advisable to bring two independently developed and implemented many-body methods to bear on the problem. DMRG is a well-established numerical technique, whose precision can be improved systematically, at the expense of increased computational effort.…”

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confidence: 99%

“…19,20 In our DMRG calculations, truncation errors were kept of the order of 10 −6 or smaller, and increasing the precision beyond this did not affect any of our conclusions. BA-LDA is a more recent development [21][22][23] ͑although the original LDA concept is, of course, widely used in ab initio calculations͒. In LDA calculations, the final precision is ultimately limited by the locality assumption inherent in the LDA, and improvements must come from the development of better functionals.…”

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confidence: 99%

Effects of nanoscale spatial inhomogeneity in strongly correlated systems

et al. 2005

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We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential v i can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction U i . Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for a reexamination of model calculations assuming spatial homogeneity. A large part of the complexity of strongly correlated systems arises from the multiple phases that coexist or compete in their phase diagrams. Metallic and insulating phases are separated by metal-insulator transitions, and subject to the formation of various types of long-range order, such as antiferromagnetism, superconductivity, and charge-or spindensity waves. The relative stability of such phases is determined by differences in appropriate thermodynamic potentials, or, at zero temperature, in their ground-state energies. Identification of the appropriate order parameters and calculation of the ground-state energies of the various phases is a complicated problem, and the nature of the phase diagram of many strongly correlated systems is still subject to considerable controversy. It is widely believed, however, that a minimal model containing the essence of strong correlations, and displaying many of the above-mentioned phases, is the homogeneous Hubbard model, which in one dimension and standard notation readsMuch theoretical effort is thus going into the analysis of the homogeneous Hubbard model and the clarification of the nature of its ground state. In a parallel development, nanoscale spatial inhomogeneity has been observed experimentally to be a ubiquitious feature of strongly correlated systems, 1-8 but although its importance is widely recognized, the consequences of such inhomogeneity are still insufficiently understood. The present paper investigates the effects of, and the competition between, two different manifestations of nanoscale inhomogeneity in strongly correlated systems, namely local variations in the on-site potential and in the on-site interaction. We base our analysis on the inhomogeneous Hubbard model

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“…In the spirit of the XC functional for the 1D Hubbard chain by Lima et al, 5,7 we choose to determine the functional within the local density approximation, first introduced by Schönhammer et al in Ref. 10.…”

Section: Determining the XC Functionalmentioning

confidence: 99%

“…4 The DFT and the Hubbard model can be combined in several ways. 5 The most obvious choices are either to determine the model parameters based on first principles calculations or to incorporate a Hubbard-type interaction into the DFT exchange-correlation functional, resulting in the so-called DFT+U method. 6 The model, however, can also be considered as an interesting system on its own and studied using DFT in a lattice formulation.…”

Section: Introductionmentioning

confidence: 99%

Lattice density-functional theory on graphene

Ijäs

Harju

2010

Phys. Rev. B

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A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

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Density-Functional Theory for the Hubbard Model: Numerical Results for the Luttinger Liquid and the Mott Insulator

Cited by 13 publications

References 58 publications

Projected site-occupation embedding theory

Projected site-occupation embedding theory

Effects of nanoscale spatial inhomogeneity in strongly correlated systems

Lattice density-functional theory on graphene

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