Density-matrix functional theory of strongly correlated lattice fermions

López-Sandoval, R.; Pastor, G.

doi:10.1103/physrevb.66.155118

Cited by 40 publications

(49 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has been recent work on the exact functional in this model from Fuks et al [8,9], Carrascal et al [10], Pastor and co-workers [11,12], Requist et al [13], and in other systems [14][15][16].…”

mentioning

confidence: 99%

Landscape of an exact energy functional

Cohen

Mori‐Sánchez

2016

Phys. Rev. A

View full text Add to dashboard Cite

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose threedimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.DOI: 10.1103/PhysRevA.93.042511In 1964 Hohenberg and Kohn [1] established density functional theory (DFT) showing that the electron density ρ is all that is is necessary to determine the exact energy of many-electron systems. However, all the challenge of electronic structure is then moved into an unknown universal functional of the density F [ρ]. For a wave function v that is the ground-state solution of the Schrödinger equation with potential v,simply subtracting off the one-electron term, gives the exactThis procedure can be carried out for many different v, to obtain many points of the exact functional F HK [ρ v ]. A question arises of whether all possible densities are achievable. This is the problem of v representability that is addressed by the constrained search by Levy and Lieb [2,3] following earlier work by Percus [4],This functional is defined for all possible densities coming from a N -electron wave function, including those that are not obtainable as the ground-state solution of a Schrödinger equation (not v representable). Once the exact functional is known, the total energy is obtained by minimization only over densities,The exact functional of the first-order density matrix γ can be derived [2,5]and used similarly, where the kinetic energy term is now a known linear functional of γ ,In this paper, the nature of the exact first-order density matrix functional is revealed by considering the asymmetric two-site Hubbard model. In this universe, the fundamental equations are tractable and the exact functional becomes a visualizable three-dimensional energy landscape in the space of density matrices. We demonstrate how this one universal landscape gives the exact energy of all possible systems, for all numbers of electrons including fractional. This connected view of the functional for all density matri...

show abstract

mentioning

confidence: 99%

Landscape of an exact energy functional

Cohen

Mori‐Sánchez

2016

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…9 A correct description of these basic properties and of the dependence of W/E HF on g 12 are at the origin of the remarkable performance of this simple dimer ansatz in the description of several ground-state properties of the Hubbard model. 17 In order to discuss the strongly correlated limit of Eq. (10) in more detail we expand W (2) to lowest order in γ 12 .…”

Section: Density-functional Theory Of Lattice Modelsmentioning

confidence: 99%

“…15 In previous papers we have formulated a lattice density functional theory (LDFT) of many-body models by considering the density matrix γ ij with respect to the lattice sites i and j as the fundamental variable. 16,17,18 The interaction energy W of the Hubbard model has been calculated exactly as a function of γ ij for various periodic lattices having γ ij = γ 12 for nearest neighbors (NNs) i and j. On this basis, a simple general approximation to W (γ 12 ) has been proposed which derives from exact dimer results, the scaling properties of W , and known limits.…”

Section: Introductionmentioning

confidence: 99%

“…Using this ansatz, several ground-state properties of one-dimensional (1D) and two-dimensional (2D) systems have been obtained in good agreement with available exact solutions and accurate numerical calculations. 17 In addition, applications to dimerized chains provided us with systematic results for the ground-state energy and charge excitation gap of the 1D Hubbard model as a function of hopping alternation and Coulomb repulsion, including the crossover from weak to strong correlations. 18 LDFT appears therefore as an efficient method of determining the electronic properties of many-body lattice models, thus encouraging further developments and applications.…”

Section: Introductionmentioning

confidence: 99%

“…III. First, we analyze the properties of a previously proposed dimer ansatz 17 and discuss its goals and limitations by comparison with known exact results. Some shortcomings of this functional in the limit of strong correlations at half-band filling are pointed out.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models

López-Sandoval

Pastor²

2004

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT).The single-particle density matrix γ ij with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional W [γ] is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of W is obtained throughout the domain of representability of γ ij , including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and threedimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for W . Goals and limitations of the different approximations are discussed.

show abstract